# bibtab

bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Altman:2020:HAE
author: Morris Altman
crossref: Bailey:2020:AVC
pages: 233--253
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_16
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Morris Altman
title:
A Holistic Approach to Empirical Analysis: The Insignificance of $P$, Hypothesis Testing and Statistical Significance*

rawtitle:
A Holistic Approach to Empirical Analysis: The Insignificance of {$P$}, Hypothesis Testing and Statistical Significance*

entry:
@InProceedings{Altman:2020:HAE,
  author =       "Morris Altman",
  title =        "A Holistic Approach to Empirical Analysis: The
                 Insignificance of {$P$}, Hypothesis Testing and
                 Statistical Significance*",
  crossref =     "Bailey:2020:AVC",
  pages =        "233--253",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_16",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: An:2020:NCS
author: Congpei An and Yuchen Xiao
title: Numerical construction of spherical $t$-designs by Barzilai--Borwein method
journal: j-APPL-NUM-MATH
volume: 150
pages: 295--302
month: apr
monthnumber: 4
year: 2020
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Tue May 12 18:18:53 MDT 2020
bibtimestamp: 2020.05.12 18:18:53 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0168927419302831
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: Congpei An and Yuchen Xiao
rawtitle: Numerical construction of spherical $t$-designs by {Barzilai--Borwein} method
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib

entry:
@Article{An:2020:NCS,
  author =       "Congpei An and Yuchen Xiao",
  title =        "Numerical construction of spherical $t$-designs by
                 {Barzilai--Borwein} method",
  journal =      j-APPL-NUM-MATH,
  volume =       "150",
  number =       "??",
  pages =        "295--302",
  month =        apr,
  year =         "2020",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Tue May 12 18:18:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927419302831",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Assis:2020:OTT
author: Michael Assis and Michael Donovan
title: Origami as a Teaching Tool for Indigenous Mathematics Education
crossref: Bailey:2020:AVC
pages: 171--188
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_12
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Michael Assis and Michael Donovan
rawtitle: Origami as a Teaching Tool for Indigenous Mathematics Education
entry:
@InProceedings{Assis:2020:OTT,
  author =       "Michael Assis and Michael Donovan",
  title =        "Origami as a Teaching Tool for Indigenous Mathematics
                 Education",
  crossref =     "Bailey:2020:AVC",
  pages =        "171--188",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_12",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Baake:2020:BCL
author: Michael Baake and Michael Coons and Neil Manibo
title: Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials
crossref: Bailey:2020:AVC
pages: 303--322
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_20
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Michael Baake and Michael Coons and Neil Ma{\~n}ibo
rawtitle: Binary Constant-Length Substitutions and {Mahler} Measures of {Borwein} Polynomials
entry:
@InProceedings{Baake:2020:BCL,
  author =       "Michael Baake and Michael Coons and Neil Ma{\~n}ibo",
  title =        "Binary Constant-Length Substitutions and {Mahler}
                 Measures of {Borwein} Polynomials",
  crossref =     "Bailey:2020:AVC",
  pages =        "303--322",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_20",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:2020:I
author: David H. Bailey and Qiji J. Zhu
title: Introduction
crossref: Bailey:2020:AVC
pages: 229--231
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_15
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Qiji J. Zhu
rawtitle: Introduction
ORCID: Bailey, David H./0000-0002-7574-8342
entry:
@InProceedings{Bailey:2020:I,
  author =       "David H. Bailey and Qiji J. Zhu",
  title =        "Introduction",
  crossref =     "Bailey:2020:AVC",
  pages =        "229--231",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_15",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: misc
filename: borwein-jonathan-m.bib
label: Bailey:2020:PBD
author: David H. Bailey
title: Peter Borwein dies at 67
pages: 229--231
day: 29
month: aug
monthnumber: 8
year: 2020
bibdate: Fri Sep 04 17:46:10 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.09.04 17:46:10 ???
URL: https://mathscholar.org/2020/08/peter-borwein-dies-at-67/
keywords: Jonathan Borwein; Peter Borwein
acknowledgement: ack-nhfb
howpublished: MathScholar Web blog.
subjectdates: Peter Benjamin Borwein (10 May 1953--23 August 2020)
rawauthor: David H. Bailey
rawtitle: {Peter Borwein} dies at 67
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Misc{Bailey:2020:PBD,
  author =       "David H. Bailey",
  title =        "{Peter Borwein} dies at 67",
  howpublished = "MathScholar Web blog.",
  day =          "29",
  month =        aug,
  year =         "2020",
  bibdate =      "Fri Sep 04 17:46:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://mathscholar.org/2020/08/peter-borwein-dies-at-67/",
  acknowledgement = ack-nhfb,
  keywords =     "Jonathan Borwein; Peter Borwein",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  subject-dates = "Peter Benjamin Borwein (10 May 1953--23 August
                 2020)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2020:ELJ
author: Naomi Simone Borwein and Judy-anne Heather Osborn
title: On the Educational Legacies of Jonathan M. Borwein
crossref: Bailey:2020:AVC
pages: 103--131
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_7
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Naomi Simone Borwein and Judy-anne Heather Osborn
rawtitle: On the Educational Legacies of {Jonathan M. Borwein}
entry:
@InProceedings{Borwein:2020:ELJ,
  author =       "Naomi Simone Borwein and Judy-anne Heather Osborn",
  title =        "On the Educational Legacies of {Jonathan M. Borwein}",
  crossref =     "Bailey:2020:AVC",
  pages =        "103--131",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_7",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2020:I
author: Naomi Simone Borwein
title: Introduction
crossref: Bailey:2020:AVC
pages: 101--102
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_6
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Naomi Simone Borwein
rawtitle: Introduction
entry:
@InProceedings{Borwein:2020:I,
  author =       "Naomi Simone Borwein",
  title =        "Introduction",
  crossref =     "Bailey:2020:AVC",
  pages =        "101--102",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_6",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Brent:2020:BBP
author: Richard P. Brent
title: The Borwein Brothers, Pi and the AGM
crossref: Bailey:2020:AVC
pages: 323--347
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_21
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Richard P. Brent
rawtitle: The {Borwein} Brothers, Pi and the {AGM}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

entry:
@InProceedings{Brent:2020:BBP,
  author =       "Richard P. Brent",
  title =        "The {Borwein} Brothers, Pi and the {AGM}",
  crossref =     "Bailey:2020:AVC",
  pages =        "323--347",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_21",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Brent:2020:I
author: Richard P. Brent
title: Introduction
crossref: Bailey:2020:AVC
pages: 299--302
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_19
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Richard P. Brent
rawtitle: Introduction
entry:
@InProceedings{Brent:2020:I,
  author =       "Richard P. Brent",
  title =        "Introduction",
  crossref =     "Bailey:2020:AVC",
  pages =        "299--302",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_19",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Burachik:2020:I
author: Regina S. Burachik and Guoyin Li
title: Introduction
crossref: Bailey:2020:AVC
pages: 3--5
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_1
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Regina S. Burachik and Guoyin Li
rawtitle: Introduction
entry:
@InProceedings{Burachik:2020:I,
  author =       "Regina S. Burachik and Guoyin Li",
  title =        "Introduction",
  crossref =     "Bailey:2020:AVC",
  pages =        "3--5",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_1",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Calude:2020:RQC
author: Cristian S. Calude and Elena Calude
title: The Road to Quantum Computational Supremacy
crossref: Bailey:2020:AVC
pages: 349--367
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_22
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Cristian S. Calude and Elena Calude
rawtitle: The Road to Quantum Computational Supremacy
entry:
@InProceedings{Calude:2020:RQC,
  author =       "Cristian S. Calude and Elena Calude",
  title =        "The Road to Quantum Computational Supremacy",
  crossref =     "Bailey:2020:AVC",
  pages =        "349--367",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_22",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Campbell:2020:HP
author: John M. Campbell and Jacopo D'Aurizio and Jonathan Sondow
title: Hypergeometry of the Parbelos
journal: j-AMER-MATH-MONTHLY
volume: 127
number: 1
pages: 23--32
year: 2020
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2020.1669403
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:45 MST 2021
bibtimestamp: 2021.12.13 15:45:45 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 19 Dec 2019
rawauthor: John M. Campbell and Jacopo D'Aurizio and Jonathan Sondow
rawtitle: Hypergeometry of the Parbelos
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib

abstract:
In the December 2013 issue of this Monthly, Sondow introduced a parabolic analog of the classical arbelos figure called the parbelos. He found that the ratio of the perimeter of an arbitrary parbelos to that of the corresponding arbelos is a constant $S$ that has an elegant symbolic evaluation involving $ 1 / pi $ and the universal parabolic constant. Using the On-Line Encyclopedia of Integer Sequences, in 2016 Campbell experimentally discovered a hypergeometric formula for $S$. Zudilin then proved the formula, using recent results of Borwein, Borwein, Glasser, and Wan on the moments of Ramanujan's generalized elliptic integrals. In the present article, we offer a variety of new proofs of Campbell's hypergeometric formula for the parbelos constant $S$, including a creative proof that makes use of a Fourier--Legendre expansion.

rawabstract:
In the December 2013 issue of this Monthly, Sondow introduced a parabolic analog of the classical arbelos figure called the parbelos. He found that the ratio of the perimeter of an arbitrary parbelos to that of the corresponding arbelos is a constant $S$ that has an elegant symbolic evaluation involving $ 1 / \pi $ and the universal parabolic constant. Using the On-Line Encyclopedia of Integer Sequences, in 2016 Campbell experimentally discovered a hypergeometric formula for $S$. Zudilin then proved the formula, using recent results of Borwein, Borwein, Glasser, and Wan on the moments of Ramanujan's generalized elliptic integrals. In the present article, we offer a variety of new proofs of Campbell's hypergeometric formula for the parbelos constant $S$, including a creative proof that makes use of a Fourier--Legendre expansion.

entry:
@Article{Campbell:2020:HP,
  author =       "John M. Campbell and Jacopo D'Aurizio and Jonathan
                 Sondow",
  title =        "Hypergeometry of the Parbelos",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "1",
  pages =        "23--32",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1669403",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:45 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  abstract =     "In the December 2013 issue of this Monthly, Sondow
                 introduced a parabolic analog of the classical arbelos
                 figure called the parbelos. He found that the ratio of
                 the perimeter of an arbitrary parbelos to that of the
                 corresponding arbelos is a constant $S$ that has an
                 elegant symbolic evaluation involving $ 1 / \pi $ and
                 the universal parabolic constant. Using the On-Line
                 Encyclopedia of Integer Sequences, in 2016 Campbell
                 experimentally discovered a hypergeometric formula for
                 $S$. Zudilin then proved the formula, using recent
                 results of Borwein, Borwein, Glasser, and Wan on the
                 moments of Ramanujan's generalized elliptic integrals.
                 In the present article, we offer a variety of new
                 proofs of Campbell's hypergeometric formula for the
                 parbelos constant $S$, including a creative proof that
                 makes use of a Fourier--Legendre expansion.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "19 Dec 2019",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Chan:2020:RWT
author: Eunice Y. S. Chan and Robert M. Corless
title: A Random Walk Through Experimental Mathematics
crossref: Bailey:2020:AVC
pages: 203--226
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_14
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Eunice Y. S. Chan and Robert M. Corless
rawtitle: A Random Walk Through Experimental Mathematics
entry:
@InProceedings{Chan:2020:RWT,
  author =       "Eunice Y. S. Chan and Robert M. Corless",
  title =        "A Random Walk Through Experimental Mathematics",
  crossref =     "Bailey:2020:AVC",
  pages =        "203--226",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_14",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Crisci:2020:SPB
author: Serena Crisci and Federica Porta and Valeria Ruggiero and Luca Zanni
journal: j-SIAM-J-OPT
volume: 30
number: 2
pages: 1300--1326
year: 2020
CODEN: SJOPE8
DOI: https://doi.org/10.1137/19M1268641
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
bibdate: Fri Mar 12 11:19:05 MST 2021
bibtimestamp: 2021.03.12 11:19:05 MST
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siopt
onlinedate: January 2020
rawauthor: Serena Crisci and Federica Porta and Valeria Ruggiero and Luca Zanni
title:
Spectral Properties of Barzilai--Borwein Rules in Solving Singly Linearly Constrained Optimization Problems Subject to Lower and Upper Bounds

bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/30/2; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjopt.bib

rawtitle:
Spectral Properties of {Barzilai--Borwein} Rules in Solving Singly Linearly Constrained Optimization Problems Subject to Lower and Upper Bounds

entry:
@Article{Crisci:2020:SPB,
  author =       "Serena Crisci and Federica Porta and Valeria Ruggiero
                 and Luca Zanni",
  title =        "Spectral Properties of {Barzilai--Borwein} Rules in
                 Solving Singly Linearly Constrained Optimization
                 Problems Subject to Lower and Upper Bounds",
  journal =      j-SIAM-J-OPT,
  volume =       "30",
  number =       "2",
  pages =        "1300--1326",
  month =        "????",
  year =         "2020",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/19M1268641",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  bibdate =      "Fri Mar 12 11:19:05 MST 2021",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/30/2;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  onlinedate =   "January 2020",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Devlin:2020:HML
author: Keith Devlin
title: How Mathematicians Learned to Stop Worrying and Love the Computer
crossref: Bailey:2020:AVC
pages: 133--139
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_8
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Keith Devlin
rawtitle: How Mathematicians Learned to Stop Worrying and Love the Computer
entry:
@InProceedings{Devlin:2020:HML,
  author =       "Keith Devlin",
  title =        "How Mathematicians Learned to Stop Worrying and Love
                 the Computer",
  crossref =     "Bailey:2020:AVC",
  pages =        "133--139",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_8",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: DiazMillan:2020:CAR
author: Reinier Diaz Millan and Scott B. Lindstrom and Vera Roshchina
title: Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples
crossref: Bailey:2020:AVC
pages: 75--98
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_5
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Reinier {D{\'\i}az Mill{\'a}n} and Scott B. Lindstrom and Vera Roshchina
rawtitle: Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples
entry:
@InProceedings{DiazMillan:2020:CAR,
  author =       "Reinier {D{\'\i}az Mill{\'a}n} and Scott B. Lindstrom
                 and Vera Roshchina",
  title =        "Comparing Averaged Relaxed Cutters and Projection
                 Methods: Theory and Examples",
  crossref =     "Bailey:2020:AVC",
  pages =        "75--98",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_5",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Dilcher:2020:NIB
author: Karl Dilcher
title: Nonlinear Identities for Bernoulli and Euler Polynomials
crossref: Bailey:2020:AVC
pages: 369--376
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_23
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Karl Dilcher
rawtitle: Nonlinear Identities for {Bernoulli} and {Euler} Polynomials
entry:
@InProceedings{Dilcher:2020:NIB,
  author =       "Karl Dilcher",
  title =        "Nonlinear Identities for {Bernoulli} and {Euler}
                 Polynomials",
  crossref =     "Bailey:2020:AVC",
  pages =        "369--376",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_23",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Dinh:2020:CRS
author: Nguyen Dinh and Miguel A. Goberna and Marco A. Lopez and Michel Volle
crossref: Bailey:2020:AVC
pages: 43--74
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_4
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Nguyen Dinh and Miguel A. Goberna and Marco A. L{\'o}pez and Michel Volle
title:
Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems

rawtitle:
Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems

entry:
@InProceedings{Dinh:2020:CRS,
  author =       "Nguyen Dinh and Miguel A. Goberna and Marco A.
                 L{\'o}pez and Michel Volle",
  title =        "Characterizations of Robust and Stable Duality for
                 Linearly Perturbed Uncertain Optimization Problems",
  crossref =     "Bailey:2020:AVC",
  pages =        "43--74",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_4",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Dolgov:2020:PCI
author: Sergey Dolgov and Dmitry Savostyanov
title: Parallel cross interpolation for high-precision calculation of high-dimensional integrals
journal: j-COMP-PHYS-COMM
volume: 246
pages: Article 106869
month: jan
monthnumber: 1
year: 2020
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2019.106869
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Tue Oct 29 14:07:57 MDT 2019
bibtimestamp: 2019.10.29 14:07:57 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465519302565
fjournal: Computer Physics Communications
remark: See cite Bailey:2006:IIC,Bailey:2015:HPA.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Sergey Dolgov and Dmitry Savostyanov
rawtitle: Parallel cross interpolation for high-precision calculation of high-dimensional integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
Cross interpolation; High precision; High-dimensional integration; Ising integrals; Ising model; Monte Carlo integration; Parallel algorithms; quasi Monte Carlo integration; Tensor train format

entry:
@Article{Dolgov:2020:PCI,
  author =       "Sergey Dolgov and Dmitry Savostyanov",
  title =        "Parallel cross interpolation for high-precision
                 calculation of high-dimensional integrals",
  journal =      j-COMP-PHYS-COMM,
  volume =       "246",
  number =       "??",
  pages =        "Article 106869",
  month =        jan,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2019.106869",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Oct 29 14:07:57 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465519302565",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "Cross interpolation; High precision; High-dimensional
                 integration; Ising integrals; Ising model; Monte Carlo
                 integration; Parallel algorithms; quasi Monte Carlo
                 integration; Tensor train format",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "See \cite{Bailey:2006:IIC,Bailey:2015:HPA}.",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Goos:2020:CBF
author: Merrilyn Goos
crossref: Bailey:2020:AVC
pages: 141--148
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_9
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Merrilyn Goos
title:
Crossing Boundaries: Fostering Collaboration Between Mathematics Educators and Mathematicians in Initial Teacher Education Programmes

rawtitle:
Crossing Boundaries: Fostering Collaboration Between Mathematics Educators and Mathematicians in Initial Teacher Education Programmes

entry:
@InProceedings{Goos:2020:CBF,
  author =       "Merrilyn Goos",
  title =        "Crossing Boundaries: Fostering Collaboration Between
                 Mathematics Educators and Mathematicians in Initial
                 Teacher Education Programmes",
  crossref =     "Bailey:2020:AVC",
  pages =        "141--148",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_9",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Holmes:2020:MEC
author: Kathryn Holmes
title: Mathematics Education in the Computational Age: Challenges and Opportunities
crossref: Bailey:2020:AVC
pages: 149--152
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_10
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Kathryn Holmes
rawtitle: Mathematics Education in the Computational Age: Challenges and Opportunities
entry:
@InProceedings{Holmes:2020:MEC,
  author =       "Kathryn Holmes",
  title =        "Mathematics Education in the Computational Age:
                 Challenges and Opportunities",
  crossref =     "Bailey:2020:AVC",
  pages =        "149--152",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_10",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Hussain:2020:MTS
author: Mumtaz Hussain and Seyyed Hassan Mahboubi and Abolfazl Seyed Motahari
title: Metrical Theory for Small Linear Forms and Applications to Interference Alignment
crossref: Bailey:2020:AVC
pages: 377--393
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_24
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Mumtaz Hussain and Seyyed Hassan Mahboubi and Abolfazl Seyed Motahari
rawtitle: Metrical Theory for Small Linear Forms and Applications to Interference Alignment
entry:
@InProceedings{Hussain:2020:MTS,
  author =       "Mumtaz Hussain and Seyyed Hassan Mahboubi and Abolfazl
                 Seyed Motahari",
  title =        "Metrical Theory for Small Linear Forms and
                 Applications to Interference Alignment",
  crossref =     "Bailey:2020:AVC",
  pages =        "377--393",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_24",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Jungic:2020:DVM
author: Damir Jungic and Veselin Jungic
title: Dynamic Visual Models: Ancient Ideas and New Technologies
crossref: Bailey:2020:AVC
pages: 189--201
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_13
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Damir Jungi{\'c} and Veselin Jungi{\'c}
rawtitle: Dynamic Visual Models: Ancient Ideas and New Technologies
entry:
@InProceedings{Jungic:2020:DVM,
  author =       "Damir Jungi{\'c} and Veselin Jungi{\'c}",
  title =        "Dynamic Visual Models: Ancient Ideas and New
                 Technologies",
  crossref =     "Bailey:2020:AVC",
  pages =        "189--201",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_13",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Phillips:2020:MEI
author: Collin Phillips and Fu Ken Ly
crossref: Bailey:2020:AVC
pages: 153--169
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_11
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Collin Phillips and Fu Ken Ly
title:
Mathematics Education for Indigenous Students in Preparation for Engineering and Information Technologies

rawtitle:
Mathematics Education for Indigenous Students in Preparation for Engineering and Information Technologies

entry:
@InProceedings{Phillips:2020:MEI,
  author =       "Collin Phillips and Fu Ken Ly",
  title =        "Mathematics Education for Indigenous Students in
                 Preparation for Engineering and Information
                 Technologies",
  crossref =     "Bailey:2020:AVC",
  pages =        "153--169",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_11",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Platt:2020:IBB
author: Dave Platt and Tim Trudgian
title: Improved Bounds on Brun's Constant
crossref: Bailey:2020:AVC
pages: 395--406
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_25
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Dave Platt and Tim Trudgian
rawtitle: Improved Bounds on {Brun}'s Constant
entry:
@InProceedings{Platt:2020:IBB,
  author =       "Dave Platt and Tim Trudgian",
  title =        "Improved Bounds on {Brun}'s Constant",
  crossref =     "Bailey:2020:AVC",
  pages =        "395--406",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_25",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Rockafellar:2020:RUD
author: R. Tyrrell Rockafellar
title: Risk and Utility in the Duality Framework of Convex Analysis
crossref: Bailey:2020:AVC
pages: 21--42
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_3
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: R. Tyrrell Rockafellar
rawtitle: Risk and Utility in the Duality Framework of Convex Analysis
entry:
@InProceedings{Rockafellar:2020:RUD,
  author =       "R. Tyrrell Rockafellar",
  title =        "Risk and Utility in the Duality Framework of Convex
                 Analysis",
  crossref =     "Bailey:2020:AVC",
  pages =        "21--42",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_3",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Skerritt:2020:EPA
author: Matthew P. Skerritt and Paul Vrbik
title: Extending the PSLQ Algorithm to Algebraic Integer Relations
crossref: Bailey:2020:AVC
pages: 407--421
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_26
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Matthew P. Skerritt and Paul Vrbik
rawtitle: Extending the {PSLQ} Algorithm to Algebraic Integer Relations
entry:
@InProceedings{Skerritt:2020:EPA,
  author =       "Matthew P. Skerritt and Paul Vrbik",
  title =        "Extending the {PSLQ} Algorithm to Algebraic Integer
                 Relations",
  crossref =     "Bailey:2020:AVC",
  pages =        "407--421",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_26",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Straub:2020:SWA
author: Armin Straub and Wadim Zudilin
title: Short Walk Adventures
crossref: Bailey:2020:AVC
pages: 423--439
year: 2020
DOI: https://doi.org/10.1007/978-3-030-36568-4_27
bibdate: Tue Apr 21 10:54:18 MDT 2020
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2020.04.21 10:54:18 MDT
acknowledgement: ack-nhfb
subjectdates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Armin Straub and Wadim Zudilin
rawtitle: Short Walk Adventures
entry:
@InProceedings{Straub:2020:SWA,
  author =       "Armin Straub and Wadim Zudilin",
  title =        "Short Walk Adventures",
  crossref =     "Bailey:2020:AVC",
  pages =        "423--439",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-36568-4_27",
  bibdate =      "Tue Apr 21 10:54:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2021:ISI
author: David H. Bailey and Scott Chapman
title: Introduction to the Special Issue
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 772--772
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1957643
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
rawauthor: David H. Bailey and Scott Chapman
rawtitle: Introduction to the Special Issue
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib

entry:
@Article{Bailey:2021:ISI,
  author =       "David H. Bailey and Scott Chapman",
  title =        "Introduction to the Special Issue",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "772--772",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1957643",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2021:JBR
author: David H. Bailey
title: Jonathan Borwein: Renaissance Mathematician
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 773--779
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1957618
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: David H. Bailey
rawtitle: {Jonathan Borwein}: {Renaissance} Mathematician
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib

entry:
@Article{Bailey:2021:JBR,
  author =       "David H. Bailey",
  title =        "{Jonathan Borwein}: {Renaissance} Mathematician",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "773--779",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1957618",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2021:EAA
author: Heinz H. Bauschke and Sylvain Gretchko and Walaa M. Moursi and Matthew Saurette
title: Edelstein's Astonishing Affine Isometry
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 796--809
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1962151
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Heinz H. Bauschke and Sylvain Gretchko and Walaa M. Moursi and Matthew Saurette
rawtitle: {Edelstein}'s Astonishing Affine Isometry
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bauschke:2021:EAA,
  author =       "Heinz H. Bauschke and Sylvain Gretchko and Walaa M.
                 Moursi and Matthew Saurette",
  title =        "{Edelstein}'s Astonishing Affine Isometry",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "796--809",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1962151",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Calkin:2021:WNM
author: Neil J. Calkin and Killian Davis and Evan Haithcock and Catherine M. Kenyon and Sylvia Wu
title: What Newton Might Have Known: Experimental Mathematics in the Classroom
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 845--855
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1964274
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Neil J. Calkin and Killian Davis and Evan Haithcock and Catherine M. Kenyon and Sylvia Wu
rawtitle: What {Newton} Might Have Known: Experimental Mathematics in the Classroom
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Calkin:2021:WNM,
  author =       "Neil J. Calkin and Killian Davis and Evan Haithcock
                 and Catherine M. Kenyon and Sylvia Wu",
  title =        "What {Newton} Might Have Known: Experimental
                 Mathematics in the Classroom",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "845--855",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1964274",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Chamberland:2021:ALE
author: Marc Chamberland and Armin Straub
title: Apery Limits: Experiments and Proofs
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 811--824
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1962153
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Marc Chamberland and Armin Straub
rawtitle: {Ap{\'e}ry} Limits: Experiments and Proofs
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Chamberland:2021:ALE,
  author =       "Marc Chamberland and Armin Straub",
  title =        "{Ap{\'e}ry} Limits: Experiments and Proofs",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "811--824",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1962153",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Chen:2021:BBG
author: Yannan Chen and Xinzhen Zhang and Yanwei Xu
journal: j-J-SCI-COMPUT
volume: 88
number: 3
pages: 65:1--65:24
month: sep
monthnumber: 9
year: 2021
CODEN: JSCOEB
DOI: https://doi.org/10.1007/s10915-021-01574-0
ISSN: 0885-7474 (print), 1573-7691 (electronic) OR 08857474 (print), 15737691 (electronic)
ISSNL: 0885-7474 OR 08857474
bibdate: Thu Feb 17 08:56:50 MST 2022
bibtimestamp: 2022.02.17 08:56:50 MST
URL: https://link.springer.com/article/10.1007/s10915-021-01574-0
fjournal: Journal of Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10915
rawauthor: Yannan Chen and Xinzhen Zhang and Yanwei Xu
title:
A Barzilai--Borwein Gradient Algorithm for Spatio-Temporal Internet Traffic Data Completion via Tensor Triple Decomposition

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib

rawtitle:
A {Barzilai--Borwein} Gradient Algorithm for Spatio-Temporal {Internet} Traffic Data Completion via Tensor Triple Decomposition

entry:
@Article{Chen:2021:BBG,
  author =       "Yannan Chen and Xinzhen Zhang and Yanwei Xu",
  title =        "A {Barzilai--Borwein} Gradient Algorithm for
                 Spatio-Temporal {Internet} Traffic Data Completion via
                 Tensor Triple Decomposition",
  journal =      j-J-SCI-COMPUT,
  volume =       "88",
  number =       "3",
  pages =        "65:1--65:24",
  month =        sep,
  year =         "2021",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1007/s10915-021-01574-0",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Thu Feb 17 08:56:50 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
  URL =          "https://link.springer.com/article/10.1007/s10915-021-01574-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: dePrado:2021:FST
author: Marcos Lopez de Prado and David H. Bailey
title: The False Strategy Theorem: A Financial Application of Experimental Mathematics
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 825--831
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1965068
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Marcos L{\'o}pez de Prado and David H. Bailey
rawtitle: The False Strategy Theorem: A Financial Application of Experimental Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{dePrado:2021:FST,
  author =       "Marcos L{\'o}pez de Prado and David H. Bailey",
  title =        "The False Strategy Theorem: A Financial Application of
                 Experimental Mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "825--831",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1965068",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Dilcher:2021:ACC
author: Karl Dilcher
title: Analytic Continuations of Character and Alternating Tornheim Zeta Functions
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 780--795
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1957617
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Karl Dilcher
rawtitle: Analytic Continuations of Character and Alternating {Tornheim} Zeta Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Dilcher:2021:ACC,
  author =       "Karl Dilcher",
  title =        "Analytic Continuations of Character and Alternating
                 {Tornheim} Zeta Functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "780--795",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1957617",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Huang:2021:EBB
author: Ya-Kui Huang and Yu-Hong Dai and Xin-Wei Liu
title: Equipping the Barzilai--Borwein Method with the Two Dimensional Quadratic Termination Property
journal: j-SIAM-J-OPT
volume: 31
number: 4
pages: 3068--3096
year: 2021
CODEN: SJOPE8
DOI: https://doi.org/10.1137/21M1390785
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
bibdate: Wed Jan 19 07:53:35 MST 2022
bibtimestamp: 2022.01.19 07:53:35 MST
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siopt
onlinedate: January 2021
rawauthor: Ya-Kui Huang and Yu-Hong Dai and Xin-Wei Liu
rawtitle: Equipping the {Barzilai--Borwein} Method with the Two Dimensional Quadratic Termination Property
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/31/4; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjopt.bib

entry:
@Article{Huang:2021:EBB,
  author =       "Ya-Kui Huang and Yu-Hong Dai and Xin-Wei Liu",
  title =        "Equipping the {Barzilai--Borwein} Method with the Two
                 Dimensional Quadratic Termination Property",
  journal =      j-SIAM-J-OPT,
  volume =       "31",
  number =       "4",
  pages =        "3068--3096",
  month =        "????",
  year =         "2021",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/21M1390785",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  bibdate =      "Wed Jan 19 07:53:35 MST 2022",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/31/4;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  onlinedate =   "January 2021",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Jungic:2021:EMM
author: Veselin Jungic and Andrijana Burazin
title: On Experimental Mathematics and Mathematics Education
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 832--844
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1964275
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Veselin Jungi{\'c} and Andrijana Burazin
rawtitle: On Experimental Mathematics and Mathematics Education
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Jungic:2021:EMM,
  author =       "Veselin Jungi{\'c} and Andrijana Burazin",
  title =        "On Experimental Mathematics and Mathematics
                 Education",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "832--844",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1964275",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Li:2021:DSP
author: Pei Heng Li and Hee Yong Youn
journal: j-J-SUPERCOMPUTING
volume: 77
number: 10
pages: 11032--11051
month: oct
monthnumber: 10
year: 2021
CODEN: JOSUED
DOI: https://doi.org/10.1007/s11227-021-03707-6
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Mon Feb 28 16:44:30 MST 2022
bibtimestamp: 2022.02.28 16:44:30 MST
URL: https://link.springer.com/article/10.1007/s11227-021-03707-6
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
ajournal: J. Supercomputing
journalURL: http://link.springer.com/journal/11227
rawauthor: Pei Heng Li and Hee Yong Youn
title:
Distributed stochastic principal component analysis using stabilized Barzilai--Borwein step-size for data compression with WSN

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/jsuper.bib

rawtitle:
Distributed stochastic principal component analysis using stabilized {Barzilai--Borwein} step-size for data compression with {WSN}

entry:
@Article{Li:2021:DSP,
  author =       "Pei Heng Li and Hee Yong Youn",
  title =        "Distributed stochastic principal component analysis
                 using stabilized {Barzilai--Borwein} step-size for data
                 compression with {WSN}",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "77",
  number =       "10",
  pages =        "11032--11051",
  month =        oct,
  year =         "2021",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-021-03707-6",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Mon Feb 28 16:44:30 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-021-03707-6",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Ponomarenko:2021:YAMi
author: Edited by Vadim Ponomarenko
title: 100 Years Ago This Month in booktitle The American Mathematical Monthly
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 855--855
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1962152
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: Edited by Vadim Ponomarenko
rawtitle: 100 Years Ago This Month in {{\booktitle{The American Mathematical Monthly}}}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Ponomarenko:2021:YAMi,
  author =       "Edited by Vadim Ponomarenko",
  title =        "100 Years Ago This Month in {{\booktitle{The American
                 Mathematical Monthly}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "855--855",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1962152",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Stoica:2021:ICC
author: George Stoica and Yousef Wardat
title: An Inequality Can Change Everything ldots
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 810--810
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1949218
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawauthor: George Stoica and Yousef Wardat
rawtitle: An Inequality Can Change Everything \ldots{}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Stoica:2021:ICC,
  author =       "George Stoica and Yousef Wardat",
  title =        "An Inequality Can Change Everything \ldots{}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "810--810",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1949218",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Ullman:2021:PSi
title: Problems and Solutions
journal: j-AMER-MATH-MONTHLY
volume: 128
number: 9
pages: 856--864
year: 2021
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2021.1964307
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Dec 13 15:45:49 MST 2021
bibtimestamp: 2021.12.13 15:45:49 MST
fjournal: American Mathematical Monthly
remark: Special issue in memory of Jonathan Borwein.
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 05 Nov 2021
rawtitle: Problems and Solutions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
Daniel H. Ullman and Daniel J. Velleman and Douglas B. West and Paul Bracken and Ezra A. Brown and Zachary Franco and George Gilbert and Laszlo Liptak and Rick Luttmann and Hosam Mahmoud and Frank B. Miles and Lenhard Ng and Rajesh Pereira and Kenneth Stolarsky and Richard Stong and Stan Wagon and Lawrence Washington and Li Zhou

rawauthor:
Daniel H. Ullman and Daniel J. Velleman and Douglas B. West and Paul Bracken and Ezra A. Brown and Zachary Franco and George Gilbert and L{\'a}szl{\'o} Lipt{\'a}k and Rick Luttmann and Hosam Mahmoud and Frank B. Miles and Lenhard Ng and Rajesh Pereira and Kenneth Stolarsky and Richard Stong and Stan Wagon and Lawrence Washington and Li Zhou

entry:
@Article{Ullman:2021:PSi,
  author =       "Daniel H. Ullman and Daniel J. Velleman and Douglas B.
                 West and Paul Bracken and Ezra A. Brown and Zachary
                 Franco and George Gilbert and L{\'a}szl{\'o} Lipt{\'a}k
                 and Rick Luttmann and Hosam Mahmoud and Frank B. Miles
                 and Lenhard Ng and Rajesh Pereira and Kenneth Stolarsky
                 and Richard Stong and Stan Wagon and Lawrence
                 Washington and Li Zhou",
  title =        "Problems and Solutions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "128",
  number =       "9",
  pages =        "856--864",
  year =         "2021",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2021.1964307",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:49 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "05 Nov 2021",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue in memory of Jonathan Borwein.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Azmi:2022:CMI
author: Behzad Azmi and Karl Kunisch
journal: j-IMA-J-NUMER-ANAL
volume: 42
number: 4
pages: 2984--3021
month: oct
monthnumber: 10
year: 2022
CODEN: IJNADH
DOI: https://doi.org/10.1093/imanum/drab056
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
bibdate: Sat Oct 22 11:06:50 MDT 2022
bibtimestamp: 2022.10.22 11:06:50 MDT
URL: http://academic.oup.com/imajna/article/42/4/2984/6340562
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: Behzad Azmi and Karl Kunisch
title:
On the convergence and mesh-independent property of the Barzilai--Borwein method for PDE-constrained optimization

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib

rawtitle:
On the convergence and mesh-independent property of the {Barzilai--Borwein} method for {PDE}-constrained optimization

entry:
@Article{Azmi:2022:CMI,
  author =       "Behzad Azmi and Karl Kunisch",
  title =        "On the convergence and mesh-independent property of
                 the {Barzilai--Borwein} method for {PDE}-constrained
                 optimization",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "42",
  number =       "4",
  pages =        "2984--3021",
  month =        oct,
  year =         "2022",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drab056",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Oct 22 11:06:50 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/42/4/2984/6340562",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Zhang:2022:BBR
author: Yaling Zhang and Hongwei Liu
journal: j-J-COMPUT-APPL-MATH
volume: 401
pages: 1--15
month: feb
monthnumber: 2
year: 2022
CODEN: JCAMDI
DOI: https://doi.org/10.1016/j.cam.2021.113781
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Mon Jan 31 08:48:37 MST 2022
bibtimestamp: 2022.01.31 08:48:37 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042721004039
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
articleno: 113781
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Yaling Zhang and Hongwei Liu
title:
A Barzilai and Borwein regularization feasible direction algorithm for convex nonlinear SOC programming with linear constraints

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib

rawtitle:
A {Barzilai} and {Borwein} regularization feasible direction algorithm for convex nonlinear {SOC} programming with linear constraints

entry:
@Article{Zhang:2022:BBR,
  author =       "Yaling Zhang and Hongwei Liu",
  title =        "A {Barzilai} and {Borwein} regularization feasible
                 direction algorithm for convex nonlinear {SOC}
                 programming with linear constraints",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "401",
  number =       "??",
  pages =        "1--15",
  month =        feb,
  year =         "2022",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2021.113781",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Mon Jan 31 08:48:37 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042721004039",
  acknowledgement = ack-nhfb,
  articleno =    "113781",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Jalilian:2024:TVM
author: Hamed Jalilian
journal: j-J-SUPERCOMPUTING
volume: 80
number: 1
pages: 601--619
month: jan
monthnumber: 1
year: 2024
CODEN: JOSUED
DOI: https://doi.org/10.1007/s11227-023-05500-z
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Thu Feb 15 10:23:12 MST 2024
bibtimestamp: 2024.02.15 10:23:12 MST
URL: https://link.springer.com/article/10.1007/s11227-023-05500-z
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
ajournal: J. Supercomputing
journalURL: http://link.springer.com/journal/11227
rawauthor: Hamed Jalilian
title:
Total variation method based on modified Barzilai--Borwein algorithm to noise reduction in MRI images

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib

rawtitle:
Total variation method based on modified {Barzilai--Borwein} algorithm to noise reduction in {MRI} images

entry:
@Article{Jalilian:2024:TVM,
  author =       "Hamed Jalilian",
  title =        "Total variation method based on modified
                 {Barzilai--Borwein} algorithm to noise reduction in
                 {MRI} images",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "80",
  number =       "1",
  pages =        "601--619",
  month =        jan,
  year =         "2024",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-023-05500-z",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Feb 15 10:23:12 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-023-05500-z",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Schaible:1981:CCP
editor: Siegfried Schaible and William T. Ziemba
booktitle: Generalized Concavity in Optimization and Economics
title: Generalized Concavity in Optimization and Economics
organization: NATO conference
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xiv + 767
year: 1981
ISBN: 0-12-621120-5 OR 0126211205
ISBN13: 978-0-12-621120-7 OR 9780126211207
LCCN: QA402.5 .G45
bibdate: Mon Mar 6 22:00:29 MST 1995
bibtimestamp: 1995.03.06 22:00:29 MST
rawbooktitle: Generalized Concavity in Optimization and Economics
raweditor: Siegfried Schaible and William T. Ziemba
rawtitle: Generalized Concavity in Optimization and Economics
note:
Papers presented at the proceedings of the NATO Advance Study Institute held at the University of British Columbia, Vancouver, Canada, August 4--15, 1980.

rawnote:
Papers presented at the proceedings of the NATO Advance Study Institute held at the University of British Columbia, Vancouver, Canada, August 4--15, 1980.

entry:
@Proceedings{Schaible:1981:CCP,
  editor =       "Siegfried Schaible and William T. Ziemba",
  booktitle =    "Generalized Concavity in Optimization and Economics",
  title =        "Generalized Concavity in Optimization and Economics",
  organization = "NATO conference",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiv + 767",
  year =         "1981",
  ISBN =         "0-12-621120-5",
  ISBN-13 =      "978-0-12-621120-7",
  LCCN =         "QA402.5 .G45",
  bibdate =      "Mon Mar 6 22:00:29 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
  note =         "Papers presented at the proceedings of the NATO
                 Advance Study Institute held at the University of
                 British Columbia, Vancouver, Canada, August 4--15,
                 1980.",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Singh:1984:ATS
editor: S. P. Singh and J. W. H. Burry and B. Watson
volume: 136
publisher: pub-SV
address: pub-SV:adr
pages: ix + 485
year: 1984
DOI: https://doi.org/10.1007/978-94-009-6466-2
ISBN: 94-009-6466-8, 94-009-6468-4 OR 9400964668, 9400964684
ISBN13: 978-94-009-6466-2, 978-94-009-6468-6 OR 9789400964662, 9789400964686
ISSN: 1389-2185 OR 13892185
bibdate: Tue Aug 16 11:51:58 MDT 2016
bibtimestamp: 2016.08.16 11:51:58 MDT
series: NATO ASI Series, Series C: Mathematical and Physical Sciences
subject: Analysis; Approximations and Expansions; Global analysis (Mathematics); Mathematics
acknowledgement: ack-nhfb
raweditor: S. P. Singh and J. W. H. Burry and B. Watson
booktitle:
Approximation Theory and Spline Functions. NATO Advanced Study Institute held at Memorial University of Newfoundland during August 22--September 2, 1983

title:
Approximation Theory and Spline Functions. NATO Advanced Study Institute held at Memorial University of Newfoundland during August 22--September 2, 1983

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

remark:
A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22--September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including Multivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invited speakers, whose contributions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at Memorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.

TOC:
Front Matter / i--ix Products of Polynomials / Bernard Beauzamy / 1--22 Exchange Algorithms, Error Estimations and Strong Unicity in Convex Programming and Chebyshev Approximation / Hans-Peter Blatt / 23--63 Four Lectures on Multivariate Approximation / E. W. Cheney / 65--87 The Approximation of Certain Functions by Compound Means / D. M. E. Foster, G. M. Phillips / 89--95 A Practical Method for Obtaining a Priori Error Bounds in Pointwise and Mean-Square Approximation Problems / Jean Meinguet / 97--125 Surface Spline Interpolation: Basic Theory and Computational Aspects / Jean Meinguet / 127--142 Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions / Charles A. Micchelli / 143--145 Semi-Norms in Polynomial Approximation / G. M. Phillips, P. J. Taylor / 147--150 On Spaces of Piecewise Polynomials in Two Variables / Larry L. Schumaker / 151--197 Birkhoff Interpolation on the Roots of Unity / A. Sharma / 199--205 Applications of Transformation Theory: A Legacy from Zolotarev (1847--1878) / John Todd / 207--245 Explicit Algebraic Nth Order Approximations to PI / J. M. Borwein, P. B. Borwein / 247--256 Solving Integral Equations of Nuclear Scattering by Splines / M. Brannigan / 257--264 $H$-Sets for Non-Linear Constrained Approximation / M. Brannigan / 265--270 Operator Pade Approximants: Some ideas behind the theory and a numerical illustration / Annie A. H. Cuyt / 271--288 Harmonic Approximation / Myron Goldstein / 289--292 Best Harmonic L1 Approximation to Subharmonic Functions / M. Goldstein, W. Haussman, K. Jetter / 293--295 B-Splines on the Circle and Trigonometric B-Splines / T. N. T. Goodman, S. L. Lee / 297--325 On Reducing the Computational Error in the Successive Approximations Method / Francois B. Guenard / 327--338 Lebesgue Constants Determined by Extremal Sets / Myron S. Henry / 339--348 Error Bounds for Interpolation by Fourth Order Trigonometric Splines / P. E. Koch / 349--360 Approximation of Derivatives in $mathbb R^n$ Application: Construction of Surfaces in $mathbb R^2$ / Alain Le Mehaute / 361--378 Meromorphic Functions, Maps and Their Rational Approximants in $mathbb C^n$ / C. H. Lutterodt / 379--396 Splines and Collocation for Ordinary Initial Value Problems / Syvert P. Norsett / 397--417 Degree of Approximation of Quasi-Hermite--Fejer Interpolation Based on Jacobi Abscissas $P_n(alpha , alpha ) (x)$ / J. Prasad, A. K. Varma / 419--440 Using Inclusion Theorems to Establish the Summability of Orthogonal Series / B. E. Rhoades / 441--453 On Projections in Approximation Theory / Boris Shekhtman / 455--466 A Survey of Exterior Asymptotics for Orthogonal Polynomials Associated with a Finite Interval and a Study of the Case of the General Weight Measures / Joseph L. Ullman / 467--478 / Back Matter / 479--485

rawbooktitle:
{Approximation Theory and Spline Functions. NATO Advanced Study Institute held at Memorial University of Newfoundland during August 22--September 2, 1983}

rawtitle:
{Approximation Theory and Spline Functions. NATO Advanced Study Institute held at Memorial University of Newfoundland during August 22--September 2, 1983}

rawTOC:
Front Matter / i--ix \\ Products of Polynomials / Bernard Beauzamy / 1--22 \\ Exchange Algorithms, Error Estimations and Strong Unicity in Convex Programming and Chebyshev Approximation / Hans-Peter Blatt / 23--63 \\ Four Lectures on Multivariate Approximation / E. W. Cheney / 65--87 \\ The Approximation of Certain Functions by Compound Means / D. M. E. Foster, G. M. Phillips / 89--95 \\ A Practical Method for Obtaining a Priori Error Bounds in Pointwise and Mean-Square Approximation Problems / Jean Meinguet / 97--125 \\ Surface Spline Interpolation: Basic Theory and Computational Aspects / Jean Meinguet / 127--142 \\ Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions / Charles A. Micchelli / 143--145 \\ Semi-Norms in Polynomial Approximation / G. M. Phillips, P. J. Taylor / 147--150 \\ On Spaces of Piecewise Polynomials in Two Variables / Larry L. Schumaker / 151--197 \\ Birkhoff Interpolation on the Roots of Unity / A. Sharma / 199--205 \\ Applications of Transformation Theory: A Legacy from Zolotarev (1847--1878) / John Todd / 207--245 \\ Explicit Algebraic Nth Order Approximations to PI / J. M. Borwein, P. B. Borwein / 247--256 \\ Solving Integral Equations of Nuclear Scattering by Splines / M. Brannigan / 257--264 \\ $H$-Sets for Non-Linear Constrained Approximation / M. Brannigan / 265--270 \\ Operator Pad{\'e} Approximants: Some ideas behind the theory and a numerical illustration / Annie A. H. Cuyt / 271--288 \\ Harmonic Approximation / Myron Goldstein / 289--292 \\ Best Harmonic L1 Approximation to Subharmonic Functions / M. Goldstein, W. Haussman, K. Jetter / 293--295 \\ B-Splines on the Circle and Trigonometric B-Splines / T. N. T. Goodman, S. L. Lee / 297--325 \\ On Reducing the Computational Error in the Successive Approximations Method / Fran{\c{c}}ois B. Gu{\'e}nard / 327--338 \\ Lebesgue Constants Determined by Extremal Sets / Myron S. Henry / 339--348 \\ Error Bounds for Interpolation by Fourth Order Trigonometric Splines / P. E. Koch / 349--360 \\ Approximation of Derivatives in $\mathbb{R}^n$ Application: Construction of Surfaces in $\mathbb{R}^2$ / Alain Le Mehaute / 361--378 \\ Meromorphic Functions, Maps and Their Rational Approximants in $\mathbb{C}^n$ / C. H. Lutterodt / 379--396 \\ Splines and Collocation for Ordinary Initial Value Problems / Syvert P. Norsett / 397--417 \\ Degree of Approximation of Quasi-Hermite--Fej{\'e}r Interpolation Based on Jacobi Abscissas $P_n(\alpha, \alpha) (x)$ / J. Prasad, A. K. Varma / 419--440 \\ Using Inclusion Theorems to Establish the Summability of Orthogonal Series / B. E. Rhoades / 441--453 \\ On Projections in Approximation Theory / Boris Shekhtman / 455--466 \\ A Survey of Exterior Asymptotics for Orthogonal Polynomials Associated with a Finite Interval and a Study of the Case of the General Weight Measures / Joseph L. Ullman / 467--478 \\ / Back Matter / 479--485

entry:
@Proceedings{Singh:1984:ATS,
  editor =       "S. P. Singh and J. W. H. Burry and B. Watson",
  booktitle =    "{Approximation Theory and Spline Functions. NATO
                 Advanced Study Institute held at Memorial University of
                 Newfoundland during August 22--September 2, 1983}",
  title =        "{Approximation Theory and Spline Functions. NATO
                 Advanced Study Institute held at Memorial University of
                 Newfoundland during August 22--September 2, 1983}",
  volume =       "136",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 485",
  year =         "1984",
  DOI =          "https://doi.org/10.1007/978-94-009-6466-2",
  ISBN =         "94-009-6466-8, 94-009-6468-4",
  ISBN-13 =      "978-94-009-6466-2, 978-94-009-6468-6",
  ISSN =         "1389-2185",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 11:51:58 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  series =       "NATO ASI Series, Series C: Mathematical and Physical
                 Sciences",
  acknowledgement = ack-nhfb,
  remark =       "A NATO Advanced Study Institute on Approximation
                 Theory and Spline Functions was held at Memorial
                 University of Newfoundland during August 22--September
                 2, 1983. This volume consists of the Proceedings of
                 that Institute. These Proceedings include the main
                 invited talks and contributed papers given during the
                 Institute. The aim of these lectures was to bring
                 together Mathematicians, Physicists and Engineers
                 working in the field. The lectures covered a wide range
                 including Multivariate Approximation, Spline Functions,
                 Rational Approximation, Applications of Elliptic
                 Integrals and Functions in the Theory of Approximation,
                 and Pad{\'e} Approximation. We express our sincere
                 thanks to Professors E. W. Cheney, J. Meinguet, J. M.
                 Phillips and H. Werner, members of the International
                 Advisory Committee. We also extend our thanks to the
                 main speakers and the invited speakers, whose
                 contributions made these Proceedings complete. The
                 Advanced Study Institute was financed by the NATO
                 Scientific Affairs Division. We express our thanks for
                 the generous support. We wish to thank members of the
                 Department of Mathematics and Statistics at Memorial
                 University who willingly helped with the planning and
                 organizing of the Institute. Special thanks go to Mrs.
                 Mary Pike who helped immensely in the planning and
                 organizing of the Institute, and to Miss Rosalind Genge
                 for her careful and excellent typing of the manuscript
                 of these Proceedings.",
  subject =      "Analysis; Approximations and Expansions; Global
                 analysis (Mathematics); Mathematics",
  tableofcontents = "Front Matter / i--ix \\
                 Products of Polynomials / Bernard Beauzamy / 1--22 \\
                 Exchange Algorithms, Error Estimations and Strong
                 Unicity in Convex Programming and Chebyshev
                 Approximation / Hans-Peter Blatt / 23--63 \\
                 Four Lectures on Multivariate Approximation / E. W.
                 Cheney / 65--87 \\
                 The Approximation of Certain Functions by Compound
                 Means / D. M. E. Foster, G. M. Phillips / 89--95 \\
                 A Practical Method for Obtaining a Priori Error Bounds
                 in Pointwise and Mean-Square Approximation Problems /
                 Jean Meinguet / 97--125 \\
                 Surface Spline Interpolation: Basic Theory and
                 Computational Aspects / Jean Meinguet / 127--142 \\
                 Interpolation of Scattered Data: Distance Matrices and
                 Conditionally Positive Definite Functions / Charles A.
                 Micchelli / 143--145 \\
                 Semi-Norms in Polynomial Approximation / G. M.
                 Phillips, P. J. Taylor / 147--150 \\
                 On Spaces of Piecewise Polynomials in Two Variables /
                 Larry L. Schumaker / 151--197 \\
                 Birkhoff Interpolation on the Roots of Unity / A.
                 Sharma / 199--205 \\
                 Applications of Transformation Theory: A Legacy from
                 Zolotarev (1847--1878) / John Todd / 207--245 \\
                 Explicit Algebraic Nth Order Approximations to PI / J.
                 M. Borwein, P. B. Borwein / 247--256 \\
                 Solving Integral Equations of Nuclear Scattering by
                 Splines / M. Brannigan / 257--264 \\
                 $H$-Sets for Non-Linear Constrained Approximation / M.
                 Brannigan / 265--270 \\
                 Operator Pad{\'e} Approximants: Some ideas behind the
                 theory and a numerical illustration / Annie A. H. Cuyt
                 / 271--288 \\
                 Harmonic Approximation / Myron Goldstein / 289--292 \\
                 Best Harmonic L1 Approximation to Subharmonic Functions
                 / M. Goldstein, W. Haussman, K. Jetter / 293--295 \\
                 B-Splines on the Circle and Trigonometric B-Splines /
                 T. N. T. Goodman, S. L. Lee / 297--325 \\
                 On Reducing the Computational Error in the Successive
                 Approximations Method / Fran{\c{c}}ois B. Gu{\'e}nard /
                 327--338 \\
                 Lebesgue Constants Determined by Extremal Sets / Myron
                 S. Henry / 339--348 \\
                 Error Bounds for Interpolation by Fourth Order
                 Trigonometric Splines / P. E. Koch / 349--360 \\
                 Approximation of Derivatives in $\mathbb{R}^n$
                 Application: Construction of Surfaces in $\mathbb{R}^2$
                 / Alain Le Mehaute / 361--378 \\
                 Meromorphic Functions, Maps and Their Rational
                 Approximants in $\mathbb{C}^n$ / C. H. Lutterodt /
                 379--396 \\
                 Splines and Collocation for Ordinary Initial Value
                 Problems / Syvert P. Norsett / 397--417 \\
                 Degree of Approximation of Quasi-Hermite--Fej{\'e}r
                 Interpolation Based on Jacobi Abscissas $P_n(\alpha,
                 \alpha) (x)$ / J. Prasad, A. K. Varma / 419--440 \\
                 Using Inclusion Theorems to Establish the Summability
                 of Orthogonal Series / B. E. Rhoades / 441--453 \\
                 On Projections in Approximation Theory / Boris
                 Shekhtman / 455--466 \\
                 A Survey of Exterior Asymptotics for Orthogonal
                 Polynomials Associated with a Finite Interval and a
                 Study of the Case of the General Weight Measures /
                 Joseph L. Ullman / 467--478 \\ / Back Matter /
                 479--485",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Andrews:1988:RRP
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xx + 609
year: 1988
ISBN: 0-12-058560-X OR 012058560X
ISBN13: 978-0-12-058560-1 OR 9780120585601
LCCN: QA1 .R26 1987
MRclass: 11A07 11F27 11F35 11K65 11N37
bibdate: Fri Sep 2 17:59:26 MDT 2022
bibtimestamp: 2022.09.02 17:59:26 MDT
remark: Twenty-eight eminent speakers presented expository talks at the Ramanujan Centenary Conference.
subject: Mathematics; Congresses; Ramanujan Aiyangar, Srinivasa
acknowledgement: ack-nhfb
subjectdates: Ramanujan (1887--1920)
editor:
George E. Andrews and Richard A. Askey and Bruce C. Berndt and K. G. Ramanathan and Robert A. Rankin and others

booktitle:
Ramanujan revisited: proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1--5, 1987

title:
Ramanujan revisited: proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1--5, 1987

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/d/dyson-freeman-j.bib; z3950.loc.gov:7090/Voyager

TOC:
List of Participants / xi Preface / xix On Ramanujan / S. Chandrasekhar / 1 A Walk Through Ramanujan's Garden / Freeman J. Dyson / 7 Combinatorial Interpretations of Ramanujan's Partition Congruences / F. G. Garvan / 29 Ramanujan's Fifth Order Mock Theta Functions as Constant Terms / George E. Andrews / 47 The Bailey Lattice: An Introduction / D. M. Bressoud / 57 Ramanujan's Identities in Statistical Mechanics / R. J. Baxter / 69 Specialized Characters for Affine Lie Algebras and the Rogers--Ramajnaun Identities / Kailash C. Misra / 85 The Exact Formula for the Weight Multiplicities of Affine Lie Algebras, I / C. J. Moreno and A. Rocha-Caridi / 111 Probabilistic Number Theory / Hubert Delange / 153 On the Number of Prime Factors of an Integer / Adolf Hildebrand / 167 Ramanujan Expansions of Arithmetical Functions / Wolfgang Schwarz / 187 On Highly Composite Numbers / Jean-Louis Nicolas / 215 Ramanujan's Tau-function and Its Generalizations / R. A. Rankin / 245 The Ramanujan $tau $ Function / M. Ram Murty / 269 Congruence Properties of $tau (n)$ / H. P. F. Swinnerton-Dyer / 289 Ramanujan's Modular Equations / Bruce C. Berndt / 313 Euler Products, Modular Identities and Elliptic Integrals in Ramanujan's Manuscripts I / S. Raghavan / 335 | Euler Products, Modular Identities and Elliptic Integrals in Ramanujan's Manuscripts II / S. S. Rangachari / 347 More Ramanujan-type Series for $1 / pi $ / J. M. Borwein and P. B. Borwein / 359 Approximations and Complex Multiplication According to Ramanujan / D. V. Chudnovsky and G. V. Chudnovsky / 375 Multiple q--Series and U(n) Generalizations of Ramanujan's $_1psi _1$ Sum / S. C. Milne / 473 Recent Results for the $q$-Lagrange Inversion Formula / Dennis Stanton / 525 Ramanujan's Second Notebook: Asymptotic Expansions for Hypergeometric Series and Related Functions / Ronald J. Evans / 561 Beta Integrals in Ramanujan's Papers, His Unpublished Work and Further Examples / Richard Askey / 561 Correlation Functions of the Selberg Integral / K. Aomoto / 591 Some Identities, for Your Amusement / R. Wm. Gosper / 607 The manuscripts for the following three lectures given at the Ramanujan Centenary Conference were unavailable for publication: Aomoto's Proof of Selberg's Integral and Constant Term Identities / Kevin Kadell / On Ramanujan's Continued Fractions / K. G. Ramanathan / Combinatorics and Continued Fractions / Gerard Viennot

rawbooktitle:
{Ramanujan revisited: proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1--5, 1987}

raweditor:
George E. Andrews and Richard A. Askey and Bruce C. Berndt and K. G. Ramanathan and Robert A. Rankin and others

rawtitle:
{Ramanujan revisited: proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1--5, 1987}

rawTOC:
List of Participants / xi \\ Preface / xix \\ On Ramanujan / S. Chandrasekhar / 1 \\ A Walk Through Ramanujan's Garden / Freeman J. Dyson / 7 \\ Combinatorial Interpretations of Ramanujan's Partition Congruences / F. G. Garvan / 29 \\ Ramanujan's Fifth Order Mock Theta Functions as Constant Terms / George E. Andrews / 47 \\ The Bailey Lattice: An Introduction / D. M. Bressoud / 57 \\ Ramanujan's Identities in Statistical Mechanics / R. J. Baxter / 69 \\ Specialized Characters for Affine Lie Algebras and the Rogers--Ramajnaun Identities / Kailash C. Misra / 85 \\ The Exact Formula for the Weight Multiplicities of Affine Lie Algebras, I / C. J. Moreno and A. Rocha-Caridi / 111 \\ Probabilistic Number Theory / Hubert Delange / 153 \\ On the Number of Prime Factors of an Integer / Adolf Hildebrand / 167 \\ Ramanujan Expansions of Arithmetical Functions / Wolfgang Schwarz / 187 \\ On Highly Composite Numbers / Jean-Louis Nicolas / 215 \\ Ramanujan's Tau-function and Its Generalizations / R. A. Rankin / 245 \\ The Ramanujan $\tau$ Function / M. Ram Murty / 269 \\ Congruence Properties of $\tau(n)$ / H. P. F. Swinnerton-Dyer / 289 \\ Ramanujan's Modular Equations / Bruce C. Berndt / 313 \\ Euler Products, Modular Identities and Elliptic Integrals in Ramanujan's Manuscripts I / S. Raghavan / 335 | Euler Products, Modular Identities and Elliptic Integrals in Ramanujan's Manuscripts II / S. S. Rangachari / 347 \\ More Ramanujan-type Series for $1 / \pi $ / J. M. Borwein and P. B. Borwein / 359 \\ Approximations and Complex Multiplication According to Ramanujan / D. V. Chudnovsky and G. V. Chudnovsky / 375 \\ Multiple q--Series and U(n) Generalizations of Ramanujan's $_1\psi_1$ Sum / S. C. Milne / 473 \\ Recent Results for the $q$-Lagrange Inversion Formula / Dennis Stanton / 525 \\ Ramanujan's Second Notebook: Asymptotic Expansions for Hypergeometric Series and Related Functions / Ronald J. Evans / 561 \\ Beta Integrals in Ramanujan's Papers, His Unpublished Work and Further Examples / Richard Askey / 561 \\ Correlation Functions of the Selberg Integral / K. Aomoto / 591 \\ Some Identities, for Your Amusement / R. Wm. Gosper / 607 \\ The manuscripts for the following three lectures given at the Ramanujan Centenary Conference were unavailable for publication: \\ Aomoto's Proof of Selberg's Integral and Constant Term Identities / Kevin Kadell / \\ On Ramanujan's Continued Fractions / K. G. Ramanathan / \\ Combinatorics and Continued Fractions / Gerard Viennot

entry:
@Proceedings{Andrews:1988:RRP,
  editor =       "George E. Andrews and Richard A. Askey and Bruce C.
                 Berndt and K. G. Ramanathan and Robert A. Rankin and
                 others",
  booktitle =    "{Ramanujan revisited: proceedings of the centenary
                 conference, University of Illinois at Urbana-Champaign,
                 June 1--5, 1987}",
  title =        "{Ramanujan revisited: proceedings of the centenary
                 conference, University of Illinois at Urbana-Champaign,
                 June 1--5, 1987}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 609",
  year =         "1988",
  ISBN =         "0-12-058560-X",
  ISBN-13 =      "978-0-12-058560-1",
  LCCN =         "QA1 .R26 1987",
  MRclass =      "11A07 11F27 11F35 11K65 11N37",
  bibdate =      "Fri Sep 2 17:59:26 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dyson-freeman-j.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "Ramanujan Centenary Conference (1987: University of
                 Illinois at Urbana-Champaign)",
  remark =       "Twenty-eight eminent speakers presented expository
                 talks at the Ramanujan Centenary Conference.",
  subject =      "Mathematics; Congresses; Ramanujan Aiyangar,
                 Srinivasa",
  subject-dates = "Ramanujan (1887--1920)",
  tableofcontents = "List of Participants / xi \\
                 Preface / xix \\
                 On Ramanujan / S. Chandrasekhar / 1 \\
                 A Walk Through Ramanujan's Garden / Freeman J. Dyson /
                 7 \\
                 Combinatorial Interpretations of Ramanujan's Partition
                 Congruences / F. G. Garvan / 29 \\
                 Ramanujan's Fifth Order Mock Theta Functions as
                 Constant Terms / George E. Andrews / 47 \\
                 The Bailey Lattice: An Introduction / D. M. Bressoud /
                 57 \\
                 Ramanujan's Identities in Statistical Mechanics / R. J.
                 Baxter / 69 \\
                 Specialized Characters for Affine Lie Algebras and the
                 Rogers--Ramajnaun Identities / Kailash C. Misra / 85
                 \\
                 The Exact Formula for the Weight Multiplicities of
                 Affine Lie Algebras, I / C. J. Moreno and A.
                 Rocha-Caridi / 111 \\
                 Probabilistic Number Theory / Hubert Delange / 153 \\
                 On the Number of Prime Factors of an Integer / Adolf
                 Hildebrand / 167 \\
                 Ramanujan Expansions of Arithmetical Functions /
                 Wolfgang Schwarz / 187 \\
                 On Highly Composite Numbers / Jean-Louis Nicolas / 215
                 \\
                 Ramanujan's Tau-function and Its Generalizations / R.
                 A. Rankin / 245 \\
                 The Ramanujan $\tau$ Function / M. Ram Murty / 269 \\
                 Congruence Properties of $\tau(n)$ / H. P. F.
                 Swinnerton-Dyer / 289 \\
                 Ramanujan's Modular Equations / Bruce C. Berndt / 313
                 \\
                 Euler Products, Modular Identities and Elliptic
                 Integrals in Ramanujan's Manuscripts I / S. Raghavan /
                 335 | Euler Products, Modular Identities and Elliptic
                 Integrals in Ramanujan's Manuscripts II / S. S.
                 Rangachari / 347 \\
                 More Ramanujan-type Series for $1 / \pi $ / J. M.
                 Borwein and P. B. Borwein / 359 \\
                 Approximations and Complex Multiplication According to
                 Ramanujan / D. V. Chudnovsky and G. V. Chudnovsky / 375
                 \\
                 Multiple q--Series and U(n) Generalizations of
                 Ramanujan's $_1\psi_1$ Sum / S. C. Milne / 473 \\
                 Recent Results for the $q$-Lagrange Inversion Formula /
                 Dennis Stanton / 525 \\
                 Ramanujan's Second Notebook: Asymptotic Expansions for
                 Hypergeometric Series and Related Functions / Ronald J.
                 Evans / 561 \\
                 Beta Integrals in Ramanujan's Papers, His Unpublished
                 Work and Further Examples / Richard Askey / 561 \\
                 Correlation Functions of the Selberg Integral / K.
                 Aomoto / 591 \\
                 Some Identities, for Your Amusement / R. Wm. Gosper /
                 607 \\
                 The manuscripts for the following three lectures given
                 at the Ramanujan Centenary Conference were unavailable
                 for publication: \\
                 Aomoto's Proof of Selberg's Integral and Constant Term
                 Identities / Kevin Kadell / \\
                 On Ramanujan's Continued Fractions / K. G. Ramanathan /
                 \\
                 Combinatorics and Continued Fractions / Gerard
                 Viennot",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Ferris:1991:WTP
editor: Timothy Ferris
booktitle: The World Treasury of Physics, Astronomy, and Mathematics
title: The World Treasury of Physics, Astronomy, and Mathematics
publisher: pub-LITTLE-BROWN
address: pub-LITTLE-BROWN:adr
pages: xv + 859
year: 1991
ISBN: 0-316-28129-8 OR 0316281298
ISBN13: 978-0-316-28129-4 OR 9780316281294
LCCN: QC71 .W67 1991
bibdate: Fri Aug 12 15:08:42 MDT 2016
bibtimestamp: 2016.08.12 15:08:42 MDT
note: With a foreword by Clifton Fadiman, general editor.
acknowledgement: ack-nhfb
rawbooktitle: The World Treasury of Physics, Astronomy, and Mathematics
raweditor: Timothy Ferris
rawnote: With a foreword by Clifton Fadiman, general editor.
rawtitle: The World Treasury of Physics, Astronomy, and Mathematics
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; https://www.math.utah.edu/pub/bibnet/authors/b/bohr-niels.bib; https://www.math.utah.edu/pub/bibnet/authors/b/born-max.bib; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/d/dyson-freeman-j.bib; https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gamow-george.bib; https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/bibnet/authors/p/planck-max.bib; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; z3950.loc.gov:7090/Voyager

abstract:
An astonishing cast of more than ninety renowned writers provides thoughtful and lucid reflections on some of the major scientific topics of our time --- from black holes and galaxies to artificial intelligence and chaos theory. Featuring essays, articles, and poems penned by notables in the worlds of both science and literature, this unique book will delight the science enthusiast and the inquisitive general reader alike.

subject:
Physics; Astronomy; Mathematics; Science; Philosophy; Physicists; Biography; Astronomers; Mathematicians; Physique; Astronomie; Mathematiques; Sciences; Philosophie; Physiciens; Biographies; Astronomes; Mathematiciens; Astronomers; Astronomy; Mathematicians; Mathematics; Physicists; Physics; Philosophy; Aufsatzsammlung; Naturwissenschaften; Physique; Astronomie; Mathematiques

TOC:
Foreword Preface Part 1: Realm of the Atom Atoms and quarks Atoms in motion / Richard P. Feynman Large and the small / Kenneth W. Ford Gay tribe of electrons / George Gamow Radioactive substances / Pierre Curie $E = m c^2$ / Albert Einstein Man who listened / Robert P. Crease and Charles C. Mann Theory of electrons and positrons / Paul A. M. Dirac Copenhagen interpretation of quantum theory / Werner Heisenberg Uncertainty and complementarity / Heinz R. Pagels Schrodinger's cat / Heinz R. Pagels Unified theory of physics / Timothy Ferris Butterflies and super strings / Freeman J. Dyson Time and space Distinction of past and future / Richard P. Feynman Second law of thermodynamics / Max Planck Age of the elements / David N. Schramm Two masses / Isaac Asimov Einstein's law of gravitation / Bertrand Russell Black holes / Roger Penrose Black holes ain't so black / Stephen W. Hawking Part 2: Wider Universe Sun and beyond Total eclipse / Annie Dillard Astride the comet / Carl Sagan and Ann Druyan Cosmic terrorist / Richard Muller I think I see it / Richard Muller Classifying the stars / Annie J. Cannon How a supernova explodes / Hans A. Bethe and Gerald Brown Measuring the universe / Harlow Shapley Milky Way galaxy / Bart J. Bok Structure of the universe Cosmology: the quest to understand the creation and expansion of the universe / Allan Sandage Exploration of space / Edwin Hubble Spherical space / Arthur Stanley Eddington Primeval atom / Georges Lemaitre New physics and the universe / James Trefil Let there be light: modern cosmogony and biblical creation / Owen Gingerich Beginnings and endings First three minutes / Steven Weinberg Magic furnace / Harald Fritzsch Origin of the universe / Alan Lightman How will the world end? / John D. Barrow and Joseph Silk Part 3: Cosmos of Numbers About mathematics Mathematician's apology / Godfrey Harold Hardy Mathematics and creativity / Alfred Adler How long is the coast of Britain? / Benoit B. Mandelbrot Chaos / James Gleick Artificial intelligence and all that Computers / Lewis Thomas Computer and the brain / John von Neumann Can a machine think? / Alan Turing Math angst Loss of certainty / Morris Kline Unreasonable effectiveness of mathematics in the natural sciences / Eugene P. Wigner What is mathematics / John D. Barrow Limits of mathematics / Philip J. Davis and Reuben Hersh Part 4: Ways of Science Scientists' lives and works Albert Einstein / John Archibald Wheeler Autobiographical notes / Albert Einstein Tribute to Max Planck / Albert Einstein Rutherford / C. P. Snow Dirac / Jagdish Mehra Hilbert / Paul A. M. Dirac Quest for order / John Tierney Legend of John von Neumann / P. R. Halmos On the beach / Andrew Hodges Ramanujan and Pi / Jonathan M. Borwein and Peter B. Borwein Paul Erdos: mathematician / Lee Dembart Man of science-Abdus Salam / Nigel Calder Two shakers of physics: memorial lecture for Sin-itiro Tomonaga / Julian Schwinger Robert Wilson and the building of Fermilab / Philip J Hilts Los Alamos / Stanislaw M. Ulam Coming into my own / Luis W. Alvarez Two cultures / C. P. Snow Women in science / Vivian Gornick Iron / Primo Levi Poetry of science When I heard the learn'd astronomer / Walt Whitman I am like a slip of comet / Gerard Manley Hopkins Arcturus / Emily Dickinson Star-swirls / Robinson Jeffers Galaxy / Richard Ryan Molecular evolution / James Clerk Maxwell Atomic architecture / A. M. Sullivan Seeing things / Howard Nemerov Cosmic gall / John Updike Nomad / Anthony Piccione Little cosmic dust poem / John Haines Connoisseur of chaos / Wallace Stevens Kings of the world / Rainer Maria Rilke Windy planet / Annie Dillard Space shuttle / Diane Ackerman Epistemology / Richard Wilbur What science says to truth / William Watson from An essay on man / Alexander Pope True enough: to the physicist / Johann Wolfgang von Goethe About Planck time / George Bradley Observatory ode / John Frederick Nims Philosophy and science Nature of science / Isaac Asimov Art of discovery / Horace Freeland Judson Structure of scientific revolutions / Thomas S. Kuhn Logic of scientific discovery / Karl Popper Causality and complementarity / Niels Bohr From Letters to Max Born / Albert Einstein Black magic and white magic / Jacob Bronowski Positivism, metaphysics, and religion / Werner Heisenberg Science and religion / Albert Einstein Acknowledgments Index

rawabstract:
An astonishing cast of more than ninety renowned writers provides thoughtful and lucid reflections on some of the major scientific topics of our time --- from black holes and galaxies to artificial intelligence and chaos theory. Featuring essays, articles, and poems penned by notables in the worlds of both science and literature, this unique book will delight the science enthusiast and the inquisitive general reader alike.

rawTOC:
Foreword \\ Preface \\ Part 1: Realm of the Atom \\ Atoms and quarks \\ Atoms in motion / Richard P. Feynman \\ Large and the small / Kenneth W. Ford \\ Gay tribe of electrons / George Gamow \\ Radioactive substances / Pierre Curie \\ $E = m c^2$ / Albert Einstein \\ Man who listened / Robert P. Crease and Charles C. Mann \\ Theory of electrons and positrons / Paul A. M. Dirac \\ Copenhagen interpretation of quantum theory / Werner Heisenberg \\ Uncertainty and complementarity / Heinz R. Pagels \\ Schrodinger's cat / Heinz R. Pagels \\ Unified theory of physics / Timothy Ferris \\ Butterflies and super strings / Freeman J. Dyson \\ Time and space \\ Distinction of past and future / Richard P. Feynman \\ Second law of thermodynamics / Max Planck \\ Age of the elements / David N. Schramm \\ Two masses / Isaac Asimov \\ Einstein's law of gravitation / Bertrand Russell \\ Black holes / Roger Penrose \\ Black holes ain't so black / Stephen W. Hawking \\ Part 2: Wider Universe \\ Sun and beyond \\ Total eclipse / Annie Dillard \\ Astride the comet / Carl Sagan and Ann Druyan \\ Cosmic terrorist / Richard Muller \\ I think I see it / Richard Muller \\ Classifying the stars / Annie J. Cannon \\ How a supernova explodes / Hans A. Bethe and Gerald Brown \\ Measuring the universe / Harlow Shapley \\ Milky Way galaxy / Bart J. Bok \\ Structure of the universe \\ Cosmology: the quest to understand the creation and expansion of the universe / Allan Sandage \\ Exploration of space / Edwin Hubble \\ Spherical space / Arthur Stanley Eddington \\ Primeval atom / Georges Lema{\^\i}tre \\ New physics and the universe / James Trefil \\ Let there be light: modern cosmogony and biblical creation / Owen Gingerich \\ Beginnings and endings \\ First three minutes / Steven Weinberg \\ Magic furnace / Harald Fritzsch \\ Origin of the universe / Alan Lightman \\ How will the world end? / John D. Barrow and Joseph Silk \\ Part 3: Cosmos of Numbers \\ About mathematics \\ Mathematician's apology / Godfrey Harold Hardy \\ Mathematics and creativity / Alfred Adler \\ How long is the coast of Britain? / Beno{\^\i}t B. Mandelbrot \\ Chaos / James Gleick \\ Artificial intelligence and all that \\ Computers / Lewis Thomas \\ Computer and the brain / John von Neumann \\ Can a machine think? / Alan Turing \\ Math angst \\ Loss of certainty / Morris Kline \\ Unreasonable effectiveness of mathematics in the natural sciences / Eugene P. Wigner \\ What is mathematics / John D. Barrow \\ Limits of mathematics / Philip J. Davis and Reuben Hersh \\ Part 4: Ways of Science \\ Scientists' lives and works \\ Albert Einstein / John Archibald Wheeler \\ Autobiographical notes / Albert Einstein \\ Tribute to Max Planck / Albert Einstein \\ Rutherford / C. P. Snow \\ Dirac / Jagdish Mehra \\ Hilbert / Paul A. M. Dirac \\ Quest for order / John Tierney \\ Legend of John von Neumann / P. R. Halmos \\ On the beach / Andrew Hodges \\ Ramanujan and Pi / Jonathan M. Borwein and Peter B. Borwein \\ Paul Erd{\H{o}}s: mathematician / Lee Dembart \\ Man of science-Abdus Salam / Nigel Calder \\ Two shakers of physics: memorial lecture for Sin-itiro Tomonaga / Julian Schwinger \\ Robert Wilson and the building of Fermilab / Philip J Hilts \\ Los Alamos / Stanislaw M. Ulam \\ Coming into my own / Luis W. Alvarez \\ Two cultures / C. P. Snow \\ Women in science / Vivian Gornick \\ Iron / Primo Levi \\ Poetry of science \\ When I heard the learn'd astronomer / Walt Whitman \\ I am like a slip of comet / Gerard Manley Hopkins \\ Arcturus / Emily Dickinson \\ Star-swirls / Robinson Jeffers \\ Galaxy / Richard Ryan \\ Molecular evolution / James Clerk Maxwell \\ Atomic architecture / A. M. Sullivan \\ Seeing things / Howard Nemerov \\ Cosmic gall / John Updike \\ Nomad / Anthony Piccione \\ Little cosmic dust poem / John Haines \\ Connoisseur of chaos / Wallace Stevens \\ Kings of the world / Rainer Maria Rilke \\ Windy planet / Annie Dillard \\ Space shuttle / Diane Ackerman \\ Epistemology / Richard Wilbur \\ What science says to truth / William Watson \\ from An essay on man / Alexander Pope \\ True enough: to the physicist / Johann Wolfgang von Goethe \\ About Planck time / George Bradley \\ Observatory ode / John Frederick Nims \\ Philosophy and science \\ Nature of science / Isaac Asimov \\ Art of discovery / Horace Freeland Judson \\ Structure of scientific revolutions / Thomas S. Kuhn \\ Logic of scientific discovery / Karl Popper \\ Causality and complementarity / Niels Bohr \\ From Letters to Max Born / Albert Einstein \\ Black magic and white magic / Jacob Bronowski \\ Positivism, metaphysics, and religion / Werner Heisenberg \\ Science and religion / Albert Einstein \\ Acknowledgments \\ Index

entry:
@Book{Ferris:1991:WTP,
  editor =       "Timothy Ferris",
  booktitle =    "The World Treasury of Physics, Astronomy, and
                 Mathematics",
  title =        "The World Treasury of Physics, Astronomy, and
                 Mathematics",
  publisher =    pub-LITTLE-BROWN,
  address =      pub-LITTLE-BROWN:adr,
  pages =        "xv + 859",
  year =         "1991",
  ISBN =         "0-316-28129-8",
  ISBN-13 =      "978-0-316-28129-4",
  LCCN =         "QC71 .W67 1991",
  bibdate =      "Fri Aug 12 15:08:42 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/b/bohr-niels.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/b/born-max.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dyson-freeman-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gamow-george.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/planck-max.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/einstein.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by Clifton Fadiman, general editor.",
  abstract =     "An astonishing cast of more than ninety renowned
                 writers provides thoughtful and lucid reflections on
                 some of the major scientific topics of our time ---
                 from black holes and galaxies to artificial
                 intelligence and chaos theory. Featuring essays,
                 articles, and poems penned by notables in the worlds of
                 both science and literature, this unique book will
                 delight the science enthusiast and the inquisitive
                 general reader alike.",
  acknowledgement = ack-nhfb,
  subject =      "Physics; Astronomy; Mathematics; Science; Philosophy;
                 Physicists; Biography; Astronomers; Mathematicians;
                 Physique; Astronomie; Math{\'e}matiques; Sciences;
                 Philosophie; Physiciens; Biographies; Astronomes;
                 Math{\'e}maticiens; Astronomers; Astronomy;
                 Mathematicians; Mathematics; Physicists; Physics;
                 Philosophy; Aufsatzsammlung; Naturwissenschaften;
                 Physique; Astronomie; Math{\'e}matiques",
  tableofcontents = "Foreword \\
                 Preface \\
                 Part 1: Realm of the Atom \\
                 Atoms and quarks \\
                 Atoms in motion / Richard P. Feynman \\
                 Large and the small / Kenneth W. Ford \\
                 Gay tribe of electrons / George Gamow \\
                 Radioactive substances / Pierre Curie \\
                 $E = m c^2$ / Albert Einstein \\
                 Man who listened / Robert P. Crease and Charles C. Mann
                 \\
                 Theory of electrons and positrons / Paul A. M. Dirac
                 \\
                 Copenhagen interpretation of quantum theory / Werner
                 Heisenberg \\
                 Uncertainty and complementarity / Heinz R. Pagels \\
                 Schrodinger's cat / Heinz R. Pagels \\
                 Unified theory of physics / Timothy Ferris \\
                 Butterflies and super strings / Freeman J. Dyson \\
                 Time and space \\
                 Distinction of past and future / Richard P. Feynman \\
                 Second law of thermodynamics / Max Planck \\
                 Age of the elements / David N. Schramm \\
                 Two masses / Isaac Asimov \\
                 Einstein's law of gravitation / Bertrand Russell \\
                 Black holes / Roger Penrose \\
                 Black holes ain't so black / Stephen W. Hawking \\
                 Part 2: Wider Universe \\
                 Sun and beyond \\
                 Total eclipse / Annie Dillard \\
                 Astride the comet / Carl Sagan and Ann Druyan \\
                 Cosmic terrorist / Richard Muller \\
                 I think I see it / Richard Muller \\
                 Classifying the stars / Annie J. Cannon \\
                 How a supernova explodes / Hans A. Bethe and Gerald
                 Brown \\
                 Measuring the universe / Harlow Shapley \\
                 Milky Way galaxy / Bart J. Bok \\
                 Structure of the universe \\
                 Cosmology: the quest to understand the creation and
                 expansion of the universe / Allan Sandage \\
                 Exploration of space / Edwin Hubble \\
                 Spherical space / Arthur Stanley Eddington \\
                 Primeval atom / Georges Lema{\^\i}tre \\
                 New physics and the universe / James Trefil \\
                 Let there be light: modern cosmogony and biblical
                 creation / Owen Gingerich \\
                 Beginnings and endings \\
                 First three minutes / Steven Weinberg \\
                 Magic furnace / Harald Fritzsch \\
                 Origin of the universe / Alan Lightman \\
                 How will the world end? / John D. Barrow and Joseph
                 Silk \\
                 Part 3: Cosmos of Numbers \\
                 About mathematics \\
                 Mathematician's apology / Godfrey Harold Hardy \\
                 Mathematics and creativity / Alfred Adler \\
                 How long is the coast of Britain? / Beno{\^\i}t B.
                 Mandelbrot \\
                 Chaos / James Gleick \\
                 Artificial intelligence and all that \\
                 Computers / Lewis Thomas \\
                 Computer and the brain / John von Neumann \\
                 Can a machine think? / Alan Turing \\
                 Math angst \\
                 Loss of certainty / Morris Kline \\
                 Unreasonable effectiveness of mathematics in the
                 natural sciences / Eugene P. Wigner \\
                 What is mathematics / John D. Barrow \\
                 Limits of mathematics / Philip J. Davis and Reuben
                 Hersh \\
                 Part 4: Ways of Science \\
                 Scientists' lives and works \\
                 Albert Einstein / John Archibald Wheeler \\
                 Autobiographical notes / Albert Einstein \\
                 Tribute to Max Planck / Albert Einstein \\
                 Rutherford / C. P. Snow \\
                 Dirac / Jagdish Mehra \\
                 Hilbert / Paul A. M. Dirac \\
                 Quest for order / John Tierney \\
                 Legend of John von Neumann / P. R. Halmos \\
                 On the beach / Andrew Hodges \\
                 Ramanujan and Pi / Jonathan M. Borwein and Peter B.
                 Borwein \\
                 Paul Erd{\H{o}}s: mathematician / Lee Dembart \\
                 Man of science-Abdus Salam / Nigel Calder \\
                 Two shakers of physics: memorial lecture for Sin-itiro
                 Tomonaga / Julian Schwinger \\
                 Robert Wilson and the building of Fermilab / Philip J
                 Hilts \\
                 Los Alamos / Stanislaw M. Ulam \\
                 Coming into my own / Luis W. Alvarez \\
                 Two cultures / C. P. Snow \\
                 Women in science / Vivian Gornick \\
                 Iron / Primo Levi \\
                 Poetry of science \\
                 When I heard the learn'd astronomer / Walt Whitman \\
                 I am like a slip of comet / Gerard Manley Hopkins \\
                 Arcturus / Emily Dickinson \\
                 Star-swirls / Robinson Jeffers \\
                 Galaxy / Richard Ryan \\
                 Molecular evolution / James Clerk Maxwell \\
                 Atomic architecture / A. M. Sullivan \\
                 Seeing things / Howard Nemerov \\
                 Cosmic gall / John Updike \\
                 Nomad / Anthony Piccione \\
                 Little cosmic dust poem / John Haines \\
                 Connoisseur of chaos / Wallace Stevens \\
                 Kings of the world / Rainer Maria Rilke \\
                 Windy planet / Annie Dillard \\
                 Space shuttle / Diane Ackerman \\
                 Epistemology / Richard Wilbur \\
                 What science says to truth / William Watson \\
                 from An essay on man / Alexander Pope \\
                 True enough: to the physicist / Johann Wolfgang von
                 Goethe \\
                 About Planck time / George Bradley \\
                 Observatory ode / John Frederick Nims \\
                 Philosophy and science \\
                 Nature of science / Isaac Asimov \\
                 Art of discovery / Horace Freeland Judson \\
                 Structure of scientific revolutions / Thomas S. Kuhn
                 \\
                 Logic of scientific discovery / Karl Popper \\
                 Causality and complementarity / Niels Bohr \\
                 From Letters to Max Born / Albert Einstein \\
                 Black magic and white magic / Jacob Bronowski \\
                 Positivism, metaphysics, and religion / Werner
                 Heisenberg \\
                 Science and religion / Albert Einstein \\
                 Acknowledgments \\
                 Index",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Ioffe:1992:ONA
editor: Aleksandr Davidovich Ioffe and Moshe Marcus and Simeon Reich
volume: 244
publisher: pub-LONGMAN
address: pub-LONGMAN:adr
pages: 315 + 2
year: 1992
ISBN: 0-582-08065-7, 0-470-21943-2 OR 0582080657, 0470219432
ISBN13: 978-0-582-08065-2, 978-0-470-21943-0 OR 9780582080652, 9780470219430
ISSN: 0269-3674 OR 02693674
LCCN: QA402.5 .O6424 1991
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Pitman research notes in mathematics series
acknowledgement: ack-nhfb
raweditor: Aleksandr Davidovich Ioffe and Moshe Marcus and Simeon Reich
booktitle:
Optimization and nonlinear analysis: [proceedings of a Binational Workshop on Optimization and Nonlinear Analysis, held at Technion City, Haifa, 21--27 March 1990]

title:
Optimization and nonlinear analysis: [proceedings of a Binational Workshop on Optimization and Nonlinear Analysis, held at Technion City, Haifa, 21--27 March 1990]

remark:
Proceedings of a Binational Workshop on Optimization and Nonlinear Analysis, held at Technion City, Haifa, 21--27 March 1990, organized by the Institute of Advanced Studies in Mathematics at the Technion and sponsored by the U.S.--Israel Binational Science Foundation and the Technion--Israel Institute of Technology.

TOC:
Foreword List of contributors Qualitative results about the convergence of convex sets and convex functions / D Aze and J-P Penot / 1 Large solutions of semilinear elliptic equations with `singular' coefficients / C Bandle and M Marcus / 25 Differentiability properties of convex, of Lipschitz, and of semicontinuous mappings on Banach spaces / J Borwein / 39 Extremal and near-extremal trajectories of rank zero in nonlinear control problems / M Briskin and Y Yomdin / 53 Integral representation theory for some classes of local functions / G Buttazzo / 64 On the use of $D$-functions in primal--dual methods and in the proximal minimization algorithm / Y Censor and S A Zenios / 76 Estimating the effect of perturbing the time delay in optimal control problems / F H Clarke and P R Wolenski / 98 Random products of nonexpansive mappings / J Dye and S Reich / 106 A primal--dual differential method for convex programming / S Flam and J Zowe / 119 Some asymptotic properties of optimal control problems with averaged performance indices considered on unbounded time intervals / V Gaitsgory / 130 On a problem concerning involutions of Banach spaces / K Goebel / 142 Dual representation of the lower second order epi-derivative of a composite function / A Ioffe / 145 Common fixed points and nonexpansive retracts / W A Kirk / 155 Variational problems on unbounded two-dimensional domains / A Leizarowitz / 169 Limits of Frechet normals in nonsmooth analysis / P D Loewen / 178 Relevance of Lavrentiev's phenomenon in 1-dimension to continuum mechanics / V J Mizel / 189 On variational analysis of differential inclusions / B S Mordukhovich / 199 Periodic points of nonexpansive operators / R D Nussbaum / 214 Nonlinear semigroups, integral equations and hyperbolic spaces / S Reich / 221 Homeomorphism conditions for normal maps of polyhedra / S M Robinson / 240 Cosmic convergence / R T Rockafellar and R J-B Wets / 249 The dynamics of some systems with hysteretic nonlinearities / T I Seidman / 273 Pontryagin maximum principle and dynamic programming for viscous hydrodynamics / S S Sritharan / 286 Optimal control theory and piecewise analyticity of the distance function for some real-analytic sub-Riemannian metrics / H J Sussmann / 298 Lagrange--Kuhn--Tucker multipliers for general mathematical programming problems / L.Thibault / 311

rawbooktitle:
{Optimization and nonlinear analysis: [proceedings of a Binational Workshop on Optimization and Nonlinear Analysis, held at Technion City, Haifa, 21--27 March 1990]}

rawtitle:
{Optimization and nonlinear analysis: [proceedings of a Binational Workshop on Optimization and Nonlinear Analysis, held at Technion City, Haifa, 21--27 March 1990]}

rawTOC:
Foreword \\ List of contributors \\ Qualitative results about the convergence of convex sets and convex functions / D Aze and J-P Penot / 1 \\ Large solutions of semilinear elliptic equations with `singular' coefficients / C Bandle and M Marcus / 25 \\ Differentiability properties of convex, of Lipschitz, and of semicontinuous mappings on Banach spaces / J Borwein / 39 \\ Extremal and near-extremal trajectories of rank zero in nonlinear control problems / M Briskin and Y Yomdin / 53 \\ Integral representation theory for some classes of local functions / G Buttazzo / 64 \\ On the use of $D$-functions in primal--dual methods and in the proximal minimization algorithm / Y Censor and S A Zenios / 76 \\ Estimating the effect of perturbing the time delay in optimal control problems / F H Clarke and P R Wolenski / 98 \\ Random products of nonexpansive mappings / J Dye and S Reich / 106 \\ A primal--dual differential method for convex programming / S Flam and J Zowe / 119 \\ Some asymptotic properties of optimal control problems with averaged performance indices considered on unbounded time intervals / V Gaitsgory / 130 \\ On a problem concerning involutions of Banach spaces / K Goebel / 142 \\ Dual representation of the lower second order epi-derivative of a composite function / A Ioffe / 145 \\ Common fixed points and nonexpansive retracts / W A Kirk / 155 \\ Variational problems on unbounded two-dimensional domains / A Leizarowitz / 169 \\ Limits of Fr{\'e}chet normals in nonsmooth analysis / P D Loewen / 178 \\ Relevance of Lavrentiev's phenomenon in 1-dimension to continuum mechanics / V J Mizel / 189 \\ On variational analysis of differential inclusions / B S Mordukhovich / 199 \\ Periodic points of nonexpansive operators / R D Nussbaum / 214 \\ Nonlinear semigroups, integral equations and hyperbolic spaces / S Reich / 221 \\ Homeomorphism conditions for normal maps of polyhedra / S M Robinson / 240 \\ Cosmic convergence / R T Rockafellar and R J-B Wets / 249 \\ The dynamics of some systems with hysteretic nonlinearities / T I Seidman / 273 \\ Pontryagin maximum principle and dynamic programming for viscous hydrodynamics / S S Sritharan / 286 \\ Optimal control theory and piecewise analyticity of the distance function for some real-analytic sub-Riemannian metrics / H J Sussmann / 298 \\ Lagrange--Kuhn--Tucker multipliers for general mathematical programming problems / L.Thibault / 311

entry:
@Proceedings{Ioffe:1992:ONA,
  editor =       "Aleksandr Davidovich Ioffe and Moshe Marcus and Simeon
                 Reich",
  booktitle =    "{Optimization and nonlinear analysis: [proceedings of
                 a Binational Workshop on Optimization and Nonlinear
                 Analysis, held at Technion City, Haifa, 21--27 March
                 1990]}",
  title =        "{Optimization and nonlinear analysis: [proceedings of
                 a Binational Workshop on Optimization and Nonlinear
                 Analysis, held at Technion City, Haifa, 21--27 March
                 1990]}",
  volume =       "244",
  publisher =    pub-LONGMAN,
  address =      pub-LONGMAN:adr,
  pages =        "315 + 2",
  year =         "1992",
  ISBN =         "0-582-08065-7, 0-470-21943-2",
  ISBN-13 =      "978-0-582-08065-2, 978-0-470-21943-0",
  ISSN =         "0269-3674",
  LCCN =         "QA402.5 .O6424 1991",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Pitman research notes in mathematics series",
  acknowledgement = ack-nhfb,
  aseries =      "Pitman Res. Notes Math. Ser.",
  remark =       "Proceedings of a Binational Workshop on Optimization
                 and Nonlinear Analysis, held at Technion City, Haifa,
                 21--27 March 1990, organized by the Institute of
                 Advanced Studies in Mathematics at the Technion and
                 sponsored by the U.S.--Israel Binational Science
                 Foundation and the Technion--Israel Institute of
                 Technology.",
  tableofcontents = "Foreword \\
                 List of contributors \\
                 Qualitative results about the convergence of convex
                 sets and convex functions / D Aze and J-P Penot / 1 \\
                 Large solutions of semilinear elliptic equations with
                 `singular' coefficients / C Bandle and M Marcus / 25
                 \\
                 Differentiability properties of convex, of Lipschitz,
                 and of semicontinuous mappings on Banach spaces / J
                 Borwein / 39 \\
                 Extremal and near-extremal trajectories of rank zero in
                 nonlinear control problems / M Briskin and Y Yomdin /
                 53 \\
                 Integral representation theory for some classes of
                 local functions / G Buttazzo / 64 \\
                 On the use of $D$-functions in primal--dual methods and
                 in the proximal minimization algorithm / Y Censor and S
                 A Zenios / 76 \\
                 Estimating the effect of perturbing the time delay in
                 optimal control problems / F H Clarke and P R Wolenski
                 / 98 \\
                 Random products of nonexpansive mappings / J Dye and S
                 Reich / 106 \\
                 A primal--dual differential method for convex
                 programming / S Flam and J Zowe / 119 \\
                 Some asymptotic properties of optimal control problems
                 with averaged performance indices considered on
                 unbounded time intervals / V Gaitsgory / 130 \\
                 On a problem concerning involutions of Banach spaces /
                 K Goebel / 142 \\
                 Dual representation of the lower second order
                 epi-derivative of a composite function / A Ioffe / 145
                 \\
                 Common fixed points and nonexpansive retracts / W A
                 Kirk / 155 \\
                 Variational problems on unbounded two-dimensional
                 domains / A Leizarowitz / 169 \\
                 Limits of Fr{\'e}chet normals in nonsmooth analysis / P
                 D Loewen / 178 \\
                 Relevance of Lavrentiev's phenomenon in 1-dimension to
                 continuum mechanics / V J Mizel / 189 \\
                 On variational analysis of differential inclusions / B
                 S Mordukhovich / 199 \\
                 Periodic points of nonexpansive operators / R D
                 Nussbaum / 214 \\
                 Nonlinear semigroups, integral equations and hyperbolic
                 spaces / S Reich / 221 \\
                 Homeomorphism conditions for normal maps of polyhedra /
                 S M Robinson / 240 \\
                 Cosmic convergence / R T Rockafellar and R J-B Wets /
                 249 \\
                 The dynamics of some systems with hysteretic
                 nonlinearities / T I Seidman / 273 \\
                 Pontryagin maximum principle and dynamic programming
                 for viscous hydrodynamics / S S Sritharan / 286 \\
                 Optimal control theory and piecewise analyticity of the
                 distance function for some real-analytic sub-Riemannian
                 metrics / H J Sussmann / 298 \\
                 Lagrange--Kuhn--Tucker multipliers for general
                 mathematical programming problems / L.Thibault / 311",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Phillips:1992:SMS
editor: Fred Young Phillips and John James Rousseau
booktitle: Systems and Management Science by Extremal Methods: Research Honoring Abraham Charnes at Age 70
title: Systems and Management Science by Extremal Methods: Research Honoring Abraham Charnes at Age 70
publisher: pub-SV
address: pub-SV:adr
pages: xxv + 580
year: 1992
DOI: https://doi.org/10.1007/978-1-4615-3600-0
ISBN: 1-4613-6599-6 (print), 1-4615-3600-6 (e-book) OR 1461365996 (print), 1461536006 (ebook)
LCCN: HD30.23
bibdate: Thu Oct 31 19:04:43 MDT 2019
bibtimestamp: 2019.10.31 19:04:43 MDT
subject: Economics; Operations research; Economics.; Operations research.
acknowledgement: ack-nhfb
rawbooktitle: Systems and Management Science by Extremal Methods: Research Honoring {Abraham Charnes} at Age 70
raweditor: Fred Young Phillips and John James Rousseau
rawtitle: Systems and Management Science by Extremal Methods: Research Honoring {Abraham Charnes} at Age 70
ISBN13:
978-1-4613-6599-0 (print), 978-1-4615-3600-0 (e-book) OR 9781461365990 (print), 9781461536000 (ebook)

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib

abstract:
This volume, booktitle Systems and Management Science by Extremal Methods, is the second in a series dedicated to honoring and extending the work of Abraham Charnes. The first volume, entitled booktitle Extremal Methods and Systems Analysis (Springer Verlag, Berlin, 1980), was edited by A. V. Fiacco and K. O. Kortanek. Subtitled ``booktitle An International Symposium on the Occasion of Abraham Charnes' Sixtieth Birthday,'' this first volume consisted of a selection from papers presented at a conference in honor of Professor Charnes held at The University of Texas at Austin in September 1977. This second volume consists of papers, to be described more fully below, that were presented in a similar conference held at the IC Institute of The University of Texas at Austin, Texas, in October of 1987, to honor Dr. Charnes on his seventieth birthday. All these papers were written by scholars and scientists whose own work has been affected by the contributions of this distinguished scholar and educator over a long period of time.

TOC:
Front Matter / i--xxv Front Matter / 1--1 Section I: Abraham Charnes --- A Record of Educational Activities 1 A Dean's Perspective on Abraham Charnes: The Nature of Creative and Innovative Research and Teaching / George Kozmetsky / 3--9 2 On Learning from Outliers / Arie Y. Lewin / 11--17 3 Abraham Charnes as Teacher and Educator: A Student's Perspective / Michael J. L. Kirby / 19--25 Front Matter / 27--27 Section II: Abraham Charnes --- A Record of Research Contributions Front Matter / 27--27 4 Contributions to Marketing / David B. Learner, Fred Y. Phillips / 29--45 5 Contributions to Human Resource Planning / Richard J. Niehaus, Edward S. Bres III / 47--68 6 Contributions to Statistics / Patrick L. Brockett, Lawrence M. Seiford / 69--88 7 Contributions to Engineering / James P. Heaney, Walter R. Lynn / 89--112 Section III: Linear Programming and Related Topics Front Matter / 113--113 8 $m$ Applications of $M$-Matrices / Abraham Berman / 115--126 9 Applications of Generalized Inverses / Adi Ben-Israel / 127--147 10 Variational Inequalities and Related Projections / Sjur D. Flaa m / 149--159 11 An Implementation and Computational Evaluation of New Criteria for the Simplex Method / Cengiz Haksever / 161--179 12 Using the Charnes et al. LP Problem Generator to Test Two Linear Programming Codes / Kenneth O. Kortanek, Jishan Zhu / 181--191 13 On the Charnes--Lemke Algorithm for Linear Programming Problems with Multipage Structure / William M. Raike, John J. Rousseau / 193--202 Section IV: Nonlinear and Probabilistically Constrained Programming Front Matter / 203--203 14 A Tutorial on Parametric Nonlinear Programming Sensitivity and Stability Analysis / Anthony V. Fiacco, Jerzy Kyparisis / 205--223 15 Topics in Input Optimization / Sanjo Zlobec / 225--243 16 Posterior Convergence Under Incomplete Information / Aharon Ben-Tal, Donald E. Brown, Robert L. Smith / 245--254 17 On $phi $-Divergence and its Applications / Marc Teboulle / 255--273 18 Spectral Estimation via Convex Programming / Aharon Ben-Tal, Jonathan M. Borwein, Marc Teboulle / 275--289 19 On Random Payoff Matrix Games / Tiantai Song / 291--308 Section V: Theory of Games, Efficiency Measurement, and Goal Programming Front Matter / 309--309 20 Homomonotone Games and Monocore Solutions / Salih O. Duffuaa, Boaz Golany / 311--326 21 Efficiency Evaluation Games / Boaz Golany, John J. Rousseau / 327--347 22 Rating Players in a Tournament: An $m$th Generation Approach / Wade D. Cook, Moshe Kress / 349--360 23 The Analytic Hierarchy Process: Structure of the Problem and its Solutions / Jonathan Barzilai, Wade D. Cook, Boaz Golany / 361--371 24 Simplified von Neumann--Morgenstern Axioms for the Subjective Valuation of Risky Assets / Crisostomo B. Garcia / 373--393 25 A Review of Policy-Bounding Techniques in Fisheries Management / William S. Lovejoy / 395--408 26 Spot Pricing of Electricity: An Appraisal of the MIT Model / Stephen C. Littlechild / 409--426 27 A Survey of Cost and Revenue Allocation Problems / Daniel Granot, Frieda Granot / 427--459 Section VI: Semi-Infinite Programming and Applications Front Matter / 461--461 28 Semi-Infinite Programming: Recent Trends of Development / Sven-AA ke Gustafson, Kenneth O. Kortanek / 463--478 29 A Recursive, Volume-Reducing Algorithm for Semi-Infinite Linear Programming / Henry Wolkowicz, Adi Ben-Israel / 479--490 30 First-and Second-Order Convex Programming Scaling Algorithms Applied to Geometric Programming / Paul R. Gribik, Siming Huang, Kenneth O. Kortanek / 491--511 31 An Optimal Stopping Game in a Restricted Market / Charles G. Bird / 513--520 32 A Mixing Routine for the Design of Hierarchical Communications Networks / George G. Polak / 521--537 Back Matter / 539--580 Appendix: Publications of Abraham Charnes

rawabstract:
This volume, \booktitle{Systems and Management Science by Extremal Methods}, is the second in a series dedicated to honoring and extending the work of Abraham Charnes. The first volume, entitled \booktitle{Extremal Methods and Systems Analysis} (Springer Verlag, Berlin, 1980), was edited by A. V. Fiacco and K. O. Kortanek. Subtitled ``\booktitle{An International Symposium on the Occasion of Abraham Charnes' Sixtieth Birthday},'' this first volume consisted of a selection from papers presented at a conference in honor of Professor Charnes held at The University of Texas at Austin in September 1977. This second volume consists of papers, to be described more fully below, that were presented in a similar conference held at the IC Institute of The University of Texas at Austin, Texas, in October of 1987, to honor Dr. Charnes on his seventieth birthday. All these papers were written by scholars and scientists whose own work has been affected by the contributions of this distinguished scholar and educator over a long period of time.

rawTOC:
Front Matter / i--xxv \\ Front Matter / 1--1 \\ Section I: Abraham Charnes --- A Record of Educational Activities \\ 1 A Dean's Perspective on Abraham Charnes: The Nature of Creative and Innovative Research and Teaching / George Kozmetsky / 3--9 \\ 2 On Learning from Outliers / Arie Y. Lewin / 11--17 \\ 3 Abraham Charnes as Teacher and Educator: A Student's Perspective / Michael J. L. Kirby / 19--25 \\ Front Matter / 27--27 \\ Section II: Abraham Charnes --- A Record of Research Contributions \\ Front Matter / 27--27 \\ 4 Contributions to Marketing / David B. Learner, Fred Y. Phillips / 29--45 \\ 5 Contributions to Human Resource Planning / Richard J. Niehaus, Edward S. Bres III / 47--68 \\ 6 Contributions to Statistics / Patrick L. Brockett, Lawrence M. Seiford / 69--88 \\ 7 Contributions to Engineering / James P. Heaney, Walter R. Lynn / 89--112 \\ Section III: Linear Programming and Related Topics \\ Front Matter / 113--113 \ 8 $m$ Applications of $M$-Matrices / Abraham Berman / 115--126 \\ 9 Applications of Generalized Inverses / Adi Ben-Israel / 127--147 \\ 10 Variational Inequalities and Related Projections / Sjur D. Fl{\aa}m / 149--159 \\ 11 An Implementation and Computational Evaluation of New Criteria for the Simplex Method / Cengiz Haksever / 161--179 \\ 12 Using the Charnes et al. LP Problem Generator to Test Two Linear Programming Codes / Kenneth O. Kortanek, Jishan Zhu / 181--191 \\ 13 On the Charnes--Lemke Algorithm for Linear Programming Problems with Multipage Structure / William M. Raike, John J. Rousseau / 193--202 \\ Section IV: Nonlinear and Probabilistically Constrained Programming \\ Front Matter / 203--203 \\ 14 A Tutorial on Parametric Nonlinear Programming Sensitivity and Stability Analysis / Anthony V. Fiacco, Jerzy Kyparisis / 205--223 \\ 15 Topics in Input Optimization / Sanjo Zlobec / 225--243 \\ 16 Posterior Convergence Under Incomplete Information / Aharon Ben-Tal, Donald E. Brown, Robert L. Smith / 245--254 \\ 17 On $\phi$-Divergence and its Applications / Marc Teboulle / 255--273 \\ 18 Spectral Estimation via Convex Programming / Aharon Ben-Tal, Jonathan M. Borwein, Marc Teboulle / 275--289 \\ 19 On Random Payoff Matrix Games / Tiantai Song / 291--308 \\ Section V: Theory of Games, Efficiency Measurement, and Goal Programming \\ Front Matter / 309--309 \\ 20 Homomonotone Games and Monocore Solutions / Salih O. Duffuaa, Boaz Golany / 311--326 \\ 21 Efficiency Evaluation Games / Boaz Golany, John J. Rousseau / 327--347 \\ 22 Rating Players in a Tournament: An $m$th Generation Approach / Wade D. Cook, Moshe Kress / 349--360 \\ 23 The Analytic Hierarchy Process: Structure of the Problem and its Solutions / Jonathan Barzilai, Wade D. Cook, Boaz Golany / 361--371 \\ 24 Simplified von Neumann--Morgenstern Axioms for the Subjective Valuation of Risky Assets / Crisostomo B. Garcia / 373--393 \\ 25 A Review of Policy-Bounding Techniques in Fisheries Management / William S. Lovejoy / 395--408 \\ 26 Spot Pricing of Electricity: An Appraisal of the MIT Model / Stephen C. Littlechild / 409--426 \\ 27 A Survey of Cost and Revenue Allocation Problems / Daniel Granot, Frieda Granot / 427--459 \\ Section VI: Semi-Infinite Programming and Applications \\ Front Matter / 461--461 \\ 28 Semi-Infinite Programming: Recent Trends of Development / Sven-{\AA}ke Gustafson, Kenneth O. Kortanek / 463--478 \\ \\ 29 A Recursive, Volume-Reducing Algorithm for Semi-Infinite Linear Programming / Henry Wolkowicz, Adi Ben-Israel / 479--490 \\ 30 First-and Second-Order Convex Programming Scaling Algorithms Applied to Geometric Programming / Paul R. Gribik, Siming Huang, Kenneth O. Kortanek / 491--511 \\ 31 An Optimal Stopping Game in a Restricted Market / Charles G. Bird / 513--520 \\ 32 A Mixing Routine for the Design of Hierarchical Communications Networks / George G. Polak / 521--537 \\ Back Matter / 539--580 \\ Appendix: Publications of Abraham Charnes

entry:
@Book{Phillips:1992:SMS,
  editor =       "Fred Young Phillips and John James Rousseau",
  booktitle =    "Systems and Management Science by Extremal Methods:
                 Research Honoring {Abraham Charnes} at Age 70",
  title =        "Systems and Management Science by Extremal Methods:
                 Research Honoring {Abraham Charnes} at Age 70",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxv + 580",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/978-1-4615-3600-0",
  ISBN =         "1-4613-6599-6 (print), 1-4615-3600-6 (e-book)",
  ISBN-13 =      "978-1-4613-6599-0 (print), 978-1-4615-3600-0
                 (e-book)",
  LCCN =         "HD30.23",
  bibdate =      "Thu Oct 31 19:04:43 MDT 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
  abstract =     "This volume, \booktitle{Systems and Management Science
                 by Extremal Methods}, is the second in a series
                 dedicated to honoring and extending the work of Abraham
                 Charnes. The first volume, entitled \booktitle{Extremal
                 Methods and Systems Analysis} (Springer Verlag, Berlin,
                 1980), was edited by A. V. Fiacco and K. O. Kortanek.
                 Subtitled ``\booktitle{An International Symposium on
                 the Occasion of Abraham Charnes' Sixtieth Birthday},''
                 this first volume consisted of a selection from papers
                 presented at a conference in honor of Professor Charnes
                 held at The University of Texas at Austin in September
                 1977. This second volume consists of papers, to be
                 described more fully below, that were presented in a
                 similar conference held at the IC Institute of The
                 University of Texas at Austin, Texas, in October of
                 1987, to honor Dr. Charnes on his seventieth birthday.
                 All these papers were written by scholars and
                 scientists whose own work has been affected by the
                 contributions of this distinguished scholar and
                 educator over a long period of time.",
  acknowledgement = ack-nhfb,
  subject =      "Economics; Operations research; Economics.; Operations
                 research.",
  tableofcontents = "Front Matter / i--xxv \\
                 Front Matter / 1--1 \\
                 Section I: Abraham Charnes --- A Record of Educational
                 Activities \\
                 1 A Dean's Perspective on Abraham Charnes: The Nature
                 of Creative and Innovative Research and Teaching /
                 George Kozmetsky / 3--9 \\
                 2 On Learning from Outliers / Arie Y. Lewin / 11--17
                 \\
                 3 Abraham Charnes as Teacher and Educator: A Student's
                 Perspective / Michael J. L. Kirby / 19--25 \\
                 Front Matter / 27--27 \\
                 Section II: Abraham Charnes --- A Record of Research
                 Contributions \\
                 Front Matter / 27--27 \\
                 4 Contributions to Marketing / David B. Learner, Fred
                 Y. Phillips / 29--45 \\
                 5 Contributions to Human Resource Planning / Richard J.
                 Niehaus, Edward S. Bres III / 47--68 \\
                 6 Contributions to Statistics / Patrick L. Brockett,
                 Lawrence M. Seiford / 69--88 \\
                 7 Contributions to Engineering / James P. Heaney,
                 Walter R. Lynn / 89--112 \\
                 Section III: Linear Programming and Related Topics \\
                 Front Matter / 113--113 \ 8 $m$ Applications of
                 $M$-Matrices / Abraham Berman / 115--126 \\
                 9 Applications of Generalized Inverses / Adi Ben-Israel
                 / 127--147 \\
                 10 Variational Inequalities and Related Projections /
                 Sjur D. Fl{\aa}m / 149--159 \\
                 11 An Implementation and Computational Evaluation of
                 New Criteria for the Simplex Method / Cengiz Haksever /
                 161--179 \\
                 12 Using the Charnes et al. LP Problem Generator to
                 Test Two Linear Programming Codes / Kenneth O.
                 Kortanek, Jishan Zhu / 181--191 \\
                 13 On the Charnes--Lemke Algorithm for Linear
                 Programming Problems with Multipage Structure / William
                 M. Raike, John J. Rousseau / 193--202 \\
                 Section IV: Nonlinear and Probabilistically Constrained
                 Programming \\
                 Front Matter / 203--203 \\
                 14 A Tutorial on Parametric Nonlinear Programming
                 Sensitivity and Stability Analysis / Anthony V. Fiacco,
                 Jerzy Kyparisis / 205--223 \\
                 15 Topics in Input Optimization / Sanjo Zlobec /
                 225--243 \\
                 16 Posterior Convergence Under Incomplete Information /
                 Aharon Ben-Tal, Donald E. Brown, Robert L. Smith /
                 245--254 \\
                 17 On $\phi$-Divergence and its Applications / Marc
                 Teboulle / 255--273 \\
                 18 Spectral Estimation via Convex Programming / Aharon
                 Ben-Tal, Jonathan M. Borwein, Marc Teboulle / 275--289
                 \\
                 19 On Random Payoff Matrix Games / Tiantai Song /
                 291--308 \\
                 Section V: Theory of Games, Efficiency Measurement, and
                 Goal Programming \\
                 Front Matter / 309--309 \\
                 20 Homomonotone Games and Monocore Solutions / Salih O.
                 Duffuaa, Boaz Golany / 311--326 \\
                 21 Efficiency Evaluation Games / Boaz Golany, John J.
                 Rousseau / 327--347 \\
                 22 Rating Players in a Tournament: An $m$th Generation
                 Approach / Wade D. Cook, Moshe Kress / 349--360 \\
                 23 The Analytic Hierarchy Process: Structure of the
                 Problem and its Solutions / Jonathan Barzilai, Wade D.
                 Cook, Boaz Golany / 361--371 \\
                 24 Simplified von Neumann--Morgenstern Axioms for the
                 Subjective Valuation of Risky Assets / Crisostomo B.
                 Garcia / 373--393 \\
                 25 A Review of Policy-Bounding Techniques in Fisheries
                 Management / William S. Lovejoy / 395--408 \\
                 26 Spot Pricing of Electricity: An Appraisal of the MIT
                 Model / Stephen C. Littlechild / 409--426 \\
                 27 A Survey of Cost and Revenue Allocation Problems /
                 Daniel Granot, Frieda Granot / 427--459 \\
                 Section VI: Semi-Infinite Programming and Applications
                 \\
                 Front Matter / 461--461 \\
                 28 Semi-Infinite Programming: Recent Trends of
                 Development / Sven-{\AA}ke Gustafson, Kenneth O.
                 Kortanek / 463--478 \\
                 \\
                 29 A Recursive, Volume-Reducing Algorithm for
                 Semi-Infinite Linear Programming / Henry Wolkowicz, Adi
                 Ben-Israel / 479--490 \\
                 30 First-and Second-Order Convex Programming Scaling
                 Algorithms Applied to Geometric Programming / Paul R.
                 Gribik, Siming Huang, Kenneth O. Kortanek / 491--511
                 \\
                 31 An Optimal Stopping Game in a Restricted Market /
                 Charles G. Bird / 513--520 \\
                 32 A Mixing Routine for the Design of Hierarchical
                 Communications Networks / George G. Polak / 521--537
                 \\
                 Back Matter / 539--580 \\
                 Appendix: Publications of Abraham Charnes",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Cohen:1995:AAA
editor: G. (Gerard) Cohen and Marc Giusti and Teo Mora
volume: 948
publisher: pub-SV
address: pub-SV:adr
pages: xi + 484
year: 1995
DOI: https://doi.org/10.1007/3-540-60114-7
ISBN: 3-540-60114-7 (softcover) OR 3540601147 (softcover)
ISBN13: 978-3-540-60114-2 (softcover) OR 9783540601142 (softcover)
LCCN: QA268 .A35 1995
bibdate: Tue Mar 14 15:37:05 MDT 2017
bibtimestamp: 2017.03.14 15:37:05 MDT
series: Lecture notes in computer science
URL: http://www.loc.gov/catdir/enhancements/fy0815/95021560-d.html
subject: Error-correcting codes (Information theory); Congresses; Algebra; Data processing; Algorithms
acknowledgement: ack-nhfb
raweditor: G. (G{\'e}rard) Cohen and Marc Giusti and Teo Mora
booktitle:
Applied algebra, algebraic algorithms, and error-correcting codes: 11th international symposium, AAECC-11, Paris, France, July 1995: proceedings

title:
Applied algebra, algebraic algorithms, and error-correcting codes: 11th international symposium, AAECC-11, Paris, France, July 1995: proceedings

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; z3950.loc.gov:7090/Voyager

abstract:
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Grobner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.

TOC:
Front Matter Supports of a code / L. A. Bassalygo / 1--3 Chemical isomerism, a challenge for algebraic combinatorics and for computer science / Ch. Benecke, R. Grund, R. Hohberger, A. Kerber, R. Laue, Th. Wieland / 4--20 On algebraic methods in covering radius problems / I. Honkala, S. Litsyn, A. Tietavainen / 21--32 How lower and upper complexity bounds meet in elimination theory / Luis M. Pardo / 33--69 Bivariate polynomial multiplication patterns / Arnold Schonhage / 70--81 Division of entire functions by polynomial ideals / J. Apel / 82--95 Variations on minimal codewords in linear codes / A. Ashikhmin, A. Barg, G. Cohen, L. Huguet / 96--105 On the computation of the radical of polynomial complete intersection ideals / Ines Armendariz, Pablo Solerno / 106--119 Which families of long binary linear codes have a binomial weight distribution? / Th. Beth, H. Kalouti, D. E. Lazic / 120--130 The discovery of simple 7-designs with automorphism group $PGamma L(2, 32)$ / Anton Betten, Adalbert Kerber, Axel Kohnert, Reinhard Laue, Alfred Wassermann / 131--145 Fast exponentiation in cryptography / Irina. E. Bocharova, Boris. D. Kudryashov / 146--157 On maximal spherical codes I / Peter Boyvalenkov, Ivan Landgev / 158--168 Formal computation of Galois groups with relative resolvents / Antoine Colin / 169--182 A case of automatic theorem proving in Euclidean geometry: the Maclane 83 theorem / Pasqualina Conti, Carlo Traverso / 183--193 Isometry classes of indecomposable linear codes / Harald Fripertinger, Adalbert Kerber / 194--204 When polynomial equation systems can be solved fast? / M. Giusti, J. Heintz, J. E. Morais, L. M. Pardo / 205--231 Using symmetric functions to describe the solution set of a zero dimensional ideal / Laureano Gonzalez-Vega, Guadalupe Trujillo / 232--247 Triangular systems and factorized Grobner bases / Hans-Gert Grabe / 248--261 Computation in algebraic function fields for effective construction of algebraic--geometric codes / Gaetan Hache / 262--278 Singly-even self-dual codes and Hadamard matrices / Masaaki Harada, Vladimir D. Tonchev / 279--284 Implicitization of curves parameterized by generalized trigonometric polynomials / Hoon Hong / 285--296 Randomness properties of partial-planes as LSI test inputs and their implementations / Yukihiro Kamiya, Takayuki Miki, Yoshihiro Iwadare / 297--311 Mixed covering codes with two binary and four ternary coordinates / E. Kolev / 312--322 About approximations of exponentials / P.-V. Koseleff / 323--333 A note on normal bases / J. Lacan, E. Delpeyroux / 334--340 On the covering radius of long Goppa codes / Francoise Levy-dit-Vehel, Simon Litsyn / 341--346 Integration of multivariate rational functions given by straight-line programs / Guillermo Matera / 347--364 Polynomial gcd computations over towers of algebraic extensions / Marc Moreno Maza, Renaud Rioboo / 365--382 Displacements of matrix products / Quyen L. Nguyen, David H. Wood / 383--392 Testing identities of series defined by algebraic partial differential equations / Ariane Peladan-Germa / 393--407 The complexity of formal resolution of linear partial differential equations / Brahim Sadik / 408--414 A fast parallel implementation of the Berlekamp--Massey algorithm with a 1D systolic array architecture / Shojiro Sakata, Masazumi Kurihara / 415--426 Tomography of constructible functions / P. Schapira / 427--435 On the determination of formal solutions of a system of partial differential equations / Jirung Albert Shih / 436--447 D4, E6, E8 and the AGM / Patrick Sole / 448--455 Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems / Annick Valibouze / 456--468 First integrals and Darboux polynomials of homogeneous linear differential systems / Jacques-Arthur Weil / 469--484 Back Matter

rawabstract:
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gr{\"o}bner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.

rawbooktitle:
{Applied algebra, algebraic algorithms, and error-correcting codes: 11th international symposium, AAECC-11, Paris, France, July 1995: proceedings}

rawtitle:
{Applied algebra, algebraic algorithms, and error-correcting codes: 11th international symposium, AAECC-11, Paris, France, July 1995: proceedings}

rawTOC:
Front Matter Supports of a code / L. A. Bassalygo / 1--3 \\ Chemical isomerism, a challenge for algebraic combinatorics and for computer science / Ch. Benecke, R. Grund, R. Hohberger, A. Kerber, R. Laue, Th. Wieland / 4--20 \\ On algebraic methods in covering radius problems / I. Honkala, S. Litsyn, A. Tiet{\"a}v{\"a}inen / 21--32 \\ How lower and upper complexity bounds meet in elimination theory / Luis M. Pardo / 33--69 \\ Bivariate polynomial multiplication patterns / Arnold Sch{\"o}nhage / 70--81 \\ Division of entire functions by polynomial ideals / J. Apel / 82--95 \\ Variations on minimal codewords in linear codes / A. Ashikhmin, A. Barg, G. Cohen, L. Huguet / 96--105 \\ On the computation of the radical of polynomial complete intersection ideals / In{\'e}s Armend{\'a}riz, Pablo Solern{\'o} / 106--119 \\ Which families of long binary linear codes have a binomial weight distribution? / Th. Beth, H. Kalouti, D. E. Lazic / 120--130 \\ The discovery of simple 7-designs with automorphism group $P\Gamma L(2, 32)$ / Anton Betten, Adalbert Kerber, Axel Kohnert, Reinhard Laue, Alfred Wassermann / 131--145 \\ Fast exponentiation in cryptography / Irina. E. Bocharova, Boris. D. Kudryashov / 146--157 \\ On maximal spherical codes I / Peter Boyvalenkov, Ivan Landgev / 158--168 \\ Formal computation of Galois groups with relative resolvents / Antoine Colin / 169--182 \\ A case of automatic theorem proving in Euclidean geometry: the Maclane 83 theorem / Pasqualina Conti, Carlo Traverso / 183--193 \\ Isometry classes of indecomposable linear codes / Harald Fripertinger, Adalbert Kerber / 194--204 \\ When polynomial equation systems can be solved fast? / M. Giusti, J. Heintz, J. E. Morais, L. M. Pardo / 205--231 \\ Using symmetric functions to describe the solution set of a zero dimensional ideal / Laureano Gonz{\'a}lez-Vega, Guadalupe Trujillo / 232--247 \\ Triangular systems and factorized Gr{\"o}bner bases / Hans-Gert Gr{\"a}be / 248--261 \\ Computation in algebraic function fields for effective construction of algebraic--geometric codes / Ga{\'e}tan Hach{\'e} / 262--278 \\ Singly-even self-dual codes and Hadamard matrices / Masaaki Harada, Vladimir D. Tonchev / 279--284 \\ Implicitization of curves parameterized by generalized trigonometric polynomials / Hoon Hong / 285--296 \\ Randomness properties of partial-planes as LSI test inputs and their implementations / Yukihiro Kamiya, Takayuki Miki, Yoshihiro Iwadare / 297--311 \\ Mixed covering codes with two binary and four ternary coordinates / E. Kolev / 312--322 \\ About approximations of exponentials / P.-V. Koseleff / 323--333 \\ A note on normal bases / J. Lacan, E. Delpeyroux / 334--340 \\ On the covering radius of long Goppa codes / Fran{\c{c}}oise Levy-dit-Vehel, Simon Litsyn / 341--346 \\ Integration of multivariate rational functions given by straight-line programs / Guillermo Matera / 347--364 \\ Polynomial gcd computations over towers of algebraic extensions / Marc Moreno Maza, Renaud Rioboo / 365--382 \\ Displacements of matrix products / Quyen L. Nguyen, David H. Wood / 383--392 \\ Testing identities of series defined by algebraic partial differential equations / Ariane P{\'e}ladan-Germa / 393--407 \\ The complexity of formal resolution of linear partial differential equations / Brahim Sadik / 408--414 \\ A fast parallel implementation of the Berlekamp--Massey algorithm with a 1D systolic array architecture / Shojiro Sakata, Masazumi Kurihara / 415--426 \\ Tomography of constructible functions / P. Schapira / 427--435 \\ On the determination of formal solutions of a system of partial differential equations / Jirung Albert Shih / 436--447 \\ D4, E6, E8 and the AGM / Patrick Sole / 448--455 \\ Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems / Annick Valibouze / 456--468 \\ First integrals and Darboux polynomials of homogeneous linear differential systems / Jacques-Arthur Weil / 469--484 \\ Back Matter

entry:
@Proceedings{Cohen:1995:AAA,
  editor =       "G. (G{\'e}rard) Cohen and Marc Giusti and Teo Mora",
  booktitle =    "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  title =        "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  volume =       "948",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 484",
  year =         "1995",
  DOI =          "https://doi.org/10.1007/3-540-60114-7",
  ISBN =         "3-540-60114-7 (softcover)",
  ISBN-13 =      "978-3-540-60114-2 (softcover)",
  LCCN =         "QA268 .A35 1995",
  bibdate =      "Tue Mar 14 15:37:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in computer science",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/95021560-d.html",
  abstract =     "This book constitutes the proceedings of the 11th
                 International Conference on Applied Algebra, Algebraic
                 Algorithms and Error-Correcting Codes, AAECC-11, held
                 in Paris, France in July 1995. The volume presents five
                 invited papers and 32 full revised research papers
                 selected from a total of 68 submissions; it is focussed
                 on research directed to the exploitation of algebraic
                 techniques and methodologies for the application in
                 coding and computer algebra. Among the topics covered
                 are coding, cryptoloy, communication, factorization of
                 polynomials, Gr{\"o}bner bases, computer algebra,
                 algebraic algorithms, symbolic computation, algebraic
                 manipulation.",
  acknowledgement = ack-nhfb,
  meetingname =  "AAECC-11 (1995 : Paris, France)",
  subject =      "Error-correcting codes (Information theory);
                 Congresses; Algebra; Data processing; Algorithms",
  tableofcontents = "Front Matter Supports of a code / L. A. Bassalygo /
                 1--3 \\
                 Chemical isomerism, a challenge for algebraic
                 combinatorics and for computer science / Ch. Benecke,
                 R. Grund, R. Hohberger, A. Kerber, R. Laue, Th. Wieland
                 / 4--20 \\
                 On algebraic methods in covering radius problems / I.
                 Honkala, S. Litsyn, A. Tiet{\"a}v{\"a}inen / 21--32 \\
                 How lower and upper complexity bounds meet in
                 elimination theory / Luis M. Pardo / 33--69 \\
                 Bivariate polynomial multiplication patterns / Arnold
                 Sch{\"o}nhage / 70--81 \\
                 Division of entire functions by polynomial ideals / J.
                 Apel / 82--95 \\
                 Variations on minimal codewords in linear codes / A.
                 Ashikhmin, A. Barg, G. Cohen, L. Huguet / 96--105 \\
                 On the computation of the radical of polynomial
                 complete intersection ideals / In{\'e}s Armend{\'a}riz,
                 Pablo Solern{\'o} / 106--119 \\
                 Which families of long binary linear codes have a
                 binomial weight distribution? / Th. Beth, H. Kalouti,
                 D. E. Lazic / 120--130 \\
                 The discovery of simple 7-designs with automorphism
                 group $P\Gamma L(2, 32)$ / Anton Betten, Adalbert
                 Kerber, Axel Kohnert, Reinhard Laue, Alfred Wassermann
                 / 131--145 \\
                 Fast exponentiation in cryptography / Irina. E.
                 Bocharova, Boris. D. Kudryashov / 146--157 \\
                 On maximal spherical codes I / Peter Boyvalenkov, Ivan
                 Landgev / 158--168 \\
                 Formal computation of Galois groups with relative
                 resolvents / Antoine Colin / 169--182 \\
                 A case of automatic theorem proving in Euclidean
                 geometry: the Maclane 83 theorem / Pasqualina Conti,
                 Carlo Traverso / 183--193 \\
                 Isometry classes of indecomposable linear codes /
                 Harald Fripertinger, Adalbert Kerber / 194--204 \\
                 When polynomial equation systems can be solved fast? /
                 M. Giusti, J. Heintz, J. E. Morais, L. M. Pardo /
                 205--231 \\
                 Using symmetric functions to describe the solution set
                 of a zero dimensional ideal / Laureano
                 Gonz{\'a}lez-Vega, Guadalupe Trujillo / 232--247 \\
                 Triangular systems and factorized Gr{\"o}bner bases /
                 Hans-Gert Gr{\"a}be / 248--261 \\
                 Computation in algebraic function fields for effective
                 construction of algebraic--geometric codes / Ga{\'e}tan
                 Hach{\'e} / 262--278 \\
                 Singly-even self-dual codes and Hadamard matrices /
                 Masaaki Harada, Vladimir D. Tonchev / 279--284 \\
                 Implicitization of curves parameterized by generalized
                 trigonometric polynomials / Hoon Hong / 285--296 \\
                 Randomness properties of partial-planes as LSI test
                 inputs and their implementations / Yukihiro Kamiya,
                 Takayuki Miki, Yoshihiro Iwadare / 297--311 \\
                 Mixed covering codes with two binary and four ternary
                 coordinates / E. Kolev / 312--322 \\
                 About approximations of exponentials / P.-V. Koseleff /
                 323--333 \\
                 A note on normal bases / J. Lacan, E. Delpeyroux /
                 334--340 \\
                 On the covering radius of long Goppa codes /
                 Fran{\c{c}}oise Levy-dit-Vehel, Simon Litsyn / 341--346
                 \\
                 Integration of multivariate rational functions given by
                 straight-line programs / Guillermo Matera / 347--364
                 \\
                 Polynomial gcd computations over towers of algebraic
                 extensions / Marc Moreno Maza, Renaud Rioboo / 365--382
                 \\
                 Displacements of matrix products / Quyen L. Nguyen,
                 David H. Wood / 383--392 \\
                 Testing identities of series defined by algebraic
                 partial differential equations / Ariane
                 P{\'e}ladan-Germa / 393--407 \\
                 The complexity of formal resolution of linear partial
                 differential equations / Brahim Sadik / 408--414 \\
                 A fast parallel implementation of the Berlekamp--Massey
                 algorithm with a 1D systolic array architecture /
                 Shojiro Sakata, Masazumi Kurihara / 415--426 \\
                 Tomography of constructible functions / P. Schapira /
                 427--435 \\
                 On the determination of formal solutions of a system of
                 partial differential equations / Jirung Albert Shih /
                 436--447 \\
                 D4, E6, E8 and the AGM / Patrick Sole / 448--455 \\
                 Computation of the Galois groups of the resolvent
                 factors for the direct and inverse Galois problems /
                 Annick Valibouze / 456--468 \\
                 First integrals and Darboux polynomials of homogeneous
                 linear differential systems / Jacques-Arthur Weil /
                 469--484 \\
                 Back Matter",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Faltings:1996:MM
author: Gerd Faltings
booktitle: Moderne Mathematik
title: Moderne Mathematik
publisher: Spectrum Akademischer Verlag
address: Heidelberg, Germany
pages: 183
year: 1996
ISBN: 3-8274-0025-2 OR 3827400252
ISBN13: 978-3-8274-0025-3 OR 9783827400253
bibdate: Fri Aug 12 14:56:49 MDT 2016
bibtimestamp: 2016.08.12 14:56:49 MDT
series: Verstandliche Forschung.
subject: Matematicas
ZMnumber: 0948.00500
acknowledgement: ack-nhfb
rawauthor: Gerd Faltings
rawbooktitle: {Moderne Mathematik}
rawtitle: {Moderne Mathematik}
keywords:
Amy Dahan; Carl Pomerance; Dalmedico Vaughan; Daniel Gorenstein; Der Beweis Aufsatzsammlung; F. R. Jones; Gabriel Wittum; Geometrie; Georg Cantor; Gerd Faltings; Gerhard Frey; Hermann Karcher; Herold M. Edwards; Jeffrey R. Weeks; John E. Hopcroft; Jonathan M. Borwein; Joseph W. Dauben; Joseph W. Sloane; Kenneth Appel; Knotentheorie; Konrad Polthier; M. Edwards Der; Marshall W. Bern; Mathematik; Mehrgitterverfahren; Minimalflache; P. Thurston Jeffrey; Peter P. Borwein; Ronald L. Graham; Sophie Germain; Spektrum; Srinivasa Ramanujan; Turingmaschine; Vierfarbensatz; William P. Thurston; Wolfgang Haken; dreidimensionale Mannigfaltigkeit; einfache Gruppe; endliche Gruppe; fermatsches Theorem; kurzes Netzwerk; matematica moderna; statistische Mechanik; verstandlich Forschung Moderne Mathematik; verstandliche Forschung

TOC:
Gerd Faltings / Einfuhrung / 7 Amy Dahan Dalmedico / Sophie Germain / 8--15 Vaughan F. R. Jones / Knotentheorie und statistische Mechanik / 16--23 Hermann Karcher and Konrad Polthier / Die Geometrie von Minimalflachen / 24--37 Gabriel Wittum / Mehrgitterverfahren / 38--51 Marshall W. Bern and Ronald L. Graham / Das Problem des kurzesten Netzwerks / 52--58 Jonathan M. Borwein and Peter B. Borwein / Srinivasa Ramanujan und die Zahl Pi / 60--68 Daniel Gorenstein / Die Klassifikation der endlichen einfachen Gruppen / 70--82 William P. Thurston and Jeffrey R. Weeks / Die Mathematik dreidimensionaler Mannigfaltigkeiten / 84--98 John E. Hopcroft / Turingmaschinen / 100--111 N. J. A. Sloane / Kugelpackungen im Raum / 112--123 Joseph W. Dauben / Georg Cantor und die Machtigkeit der Mengen / 124--134 Carl Pomerance / Primzahlen im Schnelltest / 136--146 Kenneth Appel and Wolfgang Haken / Der Beweis des Vierfarbensatzes / 148--157 Herold M. Edwards / Das Fermatsche Theorem / 158--165 Gerhard Frey / Der Beweis des Fermatschen Theorems / 166--175

rawTOC:
Gerd Faltings / Einf{\"u}hrung / 7 \\ Amy Dahan Dalmedico / Sophie Germain / 8--15 \\ Vaughan F. R. Jones / Knotentheorie und statistische Mechanik / 16--23 \\ Hermann Karcher and Konrad Polthier / Die Geometrie von Minimalflachen / 24--37 \\ Gabriel Wittum / Mehrgitterverfahren / 38--51 \\ Marshall W. Bern and Ronald L. Graham / Das Problem des kurzesten Netzwerks / 52--58 \\ Jonathan M. Borwein and Peter B. Borwein / Srinivasa Ramanujan und die Zahl Pi / 60--68 \\ Daniel Gorenstein / Die Klassifikation der endlichen einfachen Gruppen / 70--82 \\ William P. Thurston and Jeffrey R. Weeks / Die Mathematik dreidimensionaler Mannigfaltigkeiten / 84--98 \\ John E. Hopcroft / Turingmaschinen / 100--111 \\ N. J. A. Sloane / Kugelpackungen im Raum / 112--123 \\ Joseph W. Dauben / Georg Cantor und die Machtigkeit der Mengen / 124--134 \\ Carl Pomerance / Primzahlen im Schnelltest / 136--146 \\ Kenneth Appel and Wolfgang Haken / Der Beweis des Vierfarbensatzes / 148--157 \\ Herold M. Edwards / Das Fermatsche Theorem / 158--165 \\ Gerhard Frey / Der Beweis des Fermatschen Theorems / 166--175

entry:
@Book{Faltings:1996:MM,
  author =       "Gerd Faltings",
  booktitle =    "{Moderne Mathematik}",
  title =        "{Moderne Mathematik}",
  publisher =    "Spectrum Akademischer Verlag",
  address =      "Heidelberg, Germany",
  pages =        "183",
  year =         "1996",
  ISBN =         "3-8274-0025-2",
  ISBN-13 =      "978-3-8274-0025-3",
  LCCN =         "????",
  bibdate =      "Fri Aug 12 14:56:49 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Verst{\"a}ndliche Forschung.",
  ZMnumber =     "0948.00500",
  acknowledgement = ack-nhfb,
  keywords =     "Amy Dahan; Carl Pomerance; Dalmedico Vaughan; Daniel
                 Gorenstein; Der Beweis Aufsatzsammlung; F. R. Jones;
                 Gabriel Wittum; Geometrie; Georg Cantor; Gerd Faltings;
                 Gerhard Frey; Hermann Karcher; Herold M. Edwards;
                 Jeffrey R. Weeks; John E. Hopcroft; Jonathan M.
                 Borwein; Joseph W. Dauben; Joseph W. Sloane; Kenneth
                 Appel; Knotentheorie; Konrad Polthier; M. Edwards Der;
                 Marshall W. Bern; Mathematik; Mehrgitterverfahren;
                 Minimalfl{\"a}che; P. Thurston Jeffrey; Peter P.
                 Borwein; Ronald L. Graham; Sophie Germain; Spektrum;
                 Srinivasa Ramanujan; Turingmaschine; Vierfarbensatz;
                 William P. Thurston; Wolfgang Haken; dreidimensionale
                 Mannigfaltigkeit; einfache Gruppe; endliche Gruppe;
                 fermatsches Theorem; kurzes Netzwerk; matematica
                 moderna; statistische Mechanik; verst{\"a}ndlich
                 Forschung Moderne Mathematik; verst{\"a}ndliche
                 Forschung",
  subject =      "Matem{\'a}ticas",
  tableofcontents = "Gerd Faltings / Einf{\"u}hrung / 7 \\
                 Amy Dahan Dalmedico / Sophie Germain / 8--15 \\
                 Vaughan F. R. Jones / Knotentheorie und statistische
                 Mechanik / 16--23 \\
                 Hermann Karcher and Konrad Polthier / Die Geometrie von
                 Minimalflachen / 24--37 \\
                 Gabriel Wittum / Mehrgitterverfahren / 38--51 \\
                 Marshall W. Bern and Ronald L. Graham / Das Problem des
                 kurzesten Netzwerks / 52--58 \\
                 Jonathan M. Borwein and Peter B. Borwein / Srinivasa
                 Ramanujan und die Zahl Pi / 60--68 \\
                 Daniel Gorenstein / Die Klassifikation der endlichen
                 einfachen Gruppen / 70--82 \\
                 William P. Thurston and Jeffrey R. Weeks / Die
                 Mathematik dreidimensionaler Mannigfaltigkeiten /
                 84--98 \\
                 John E. Hopcroft / Turingmaschinen / 100--111 \\
                 N. J. A. Sloane / Kugelpackungen im Raum / 112--123 \\
                 Joseph W. Dauben / Georg Cantor und die Machtigkeit der
                 Mengen / 124--134 \\
                 Carl Pomerance / Primzahlen im Schnelltest / 136--146
                 \\
                 Kenneth Appel and Wolfgang Haken / Der Beweis des
                 Vierfarbensatzes / 148--157 \\
                 Herold M. Edwards / Das Fermatsche Theorem / 158--165
                 \\
                 Gerhard Frey / Der Beweis des Fermatschen Theorems /
                 166--175",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Berggren:1997:PSB
editor: Lennart Berggren and Jonathan M. Borwein and Peter B. Borwein
booktitle: Pi, a source book
title: Pi, a source book
publisher: pub-SV
address: pub-SV:adr
pages: xix + 716
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4
LCCN: QA484 .P5 1997
bibdate: Fri Sep 2 17:41:50 MDT 2022
bibtimestamp: 2022.09.02 17:41:50 MDT
subject: Pi; Pi (Le nombre); Pi.; Pi (le nombre)
acknowledgement: ack-nhfb
rawbooktitle: Pi, a source book
raweditor: Lennart Berggren and Jonathan M. Borwein and Peter B. Borwein
rawtitle: Pi, a source book
ORCID: Borwein, Jonathan/0000-0002-1263-0646
ISBN:
0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0 (print), 3-540-94924-0 OR 0387949240, 1475727364 (ebook), 1475727380 (print), 3540949240

ISBN13:
978-0-387-94924-6, 978-1-4757-2736-4 (e-book), 978-1-4757-2738-8 (print), 978-3-540-94924-4 OR 9780387949246, 9781475727364 (ebook), 9781475727388 (print), 9783540949244

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib; z3950.loc.gov:7090/Voyager

abstract:
The aim of this book is to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics, and a surprising amount of the most important mathematics and mathematicians have contributed to its unfolding. Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. Yet, despite this, no source book on pi has been published. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet still accessible, mathematics. Mathematicians and historians of mathematics will find this book indispensable. Teachers at every level from the seventh grade onward will find here ample resources for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: first a selection of the mathematical literature of four millennia, second a variety of historical studies or writings on the cultural meaning and significance of the number, and third, a number of treatments on pi that are fanciful, satirical and/or whimsical.

TOC:
Preface / v Acknowledgments / ix Introduction / xvii 1. The Rhind Mathematical Papyrus-Problem 50 ($approx $ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 3. Archimedes. Measurement of a Circle ($approx $ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $pi $ / 7 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $pi $ using modern notation / 15 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $pi $ and also examines values for $pi $ given by Zu Chongzhi (429--500) / 20 6. The Banu Musa: The Measurement of Plane and Solid Figures ($approx $ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 7. Madhava. The Power Series for Arctan and Pi ($approx $ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $pi $ / 45 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $pi $ / 51 9. Viete. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 10. Wallis. Computation of $pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $pi $ that bears his name / 68 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/pi $ / 78 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 14. Roy. The Discovery of the Series Formula for $pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $pi /4 = 1 - 1/3 + 1/5, cdots $ / 92 15. Jones. The First Use of $pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $pi $ to 16 decimal places / 110 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $pi $ and powers of $pi $ / 112 18. Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $pi $ / 129 19. Lambert. Irrationality of $pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $pi $ / 141 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $pi $ / 147 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 22. Lindemann. Ueber die Zahl $pi $ (1882) / The first proof of the transcendence of $pi $ / 194 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $pi $ / 207 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $pi $ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $pi $ / 226 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $pi $ in Indiana / 230 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $pi $ (including a copy of the actual bill that was proposed) / 231 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $pi $ / 236 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $pi $ / 240 29. Ramanujan. Modular Equations and Approximations to $pi $ (1914) / Ramanujan's seminal paper on $pi $ that includes a number of striking series and algebraic approximations / 241 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 31. Ballantine. The Best (?) Formula for Computing $pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $pi $ more cleverly / 271 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $pi / 4 $ as a sum of arctan relations in powers of 10 / 274 33. Niven. A Simple Proof that $pi $ Is Irrational (1947) / A very concise proof of the irrationality of $pi $ / 276 34. Reitwiesner. An ENIAC Determination of $pi $ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $pi $ from 3000 BC to 1949 / 282 36. Mahler. On the Approximation of $pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $pi $ from a given rational or algebraic number'' / 306 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $pi $ (1960) / A history of the calculation of the digits of $pi $ to 1960 38. Shanks and Wrench, Jr. Calculation of $pi $ to 100,000 Decimals (1962) / A landmark computation of $pi $ to more than 100,000 places / 326 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $pi $ / 400 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $pi $ / 402 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 48. Beukers. A Note on the Irrationality of $zeta (2)$ and $zetq (3)$ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $zeta (3)$ (and $zeta (2)$) / 434 49. van der Poorten. A Proof that Euler Missed ldots Apery's Proof of the Irrationality of $zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $zeta (3)$ / 439 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 51. Apostol. A Proof that Euler Missed: Evaluating $zeta (2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $zeta (2) = pi / 6$ / 456 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 53. Stern. A Remarkable Approximation to $pi $ (1985) / Justification of the value of $pi $ in the Bible through numerological interpretations / 460 54. Newman and Shanks. On a Sequence Arising in Series for $pi $ (1984) / More connections between $pi $ and modular equations / 462 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $pi $) / 537 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $pi $ using the Gauss AGM without explicit elliptic function theory / 553 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $pi $ has randomly distributed digits / 557 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $pi $ / 560 60. Bailey. The Computation of $pi $ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $pi $ and for performing the required multiple-precision arithmetic / 562 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $pi $ / 576 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $pi $, and how his approach is now incorporated into modern computer algorithms / 588 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $pi $ using mathematics rooted in Ramanujan's work / 623 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $pi $, truncated at 500,000 terms, gives $pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 66. Beukers, Bezivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 67. Webster. The Tail of Pi (1991) / Various anecdotes about $pi $ from the 14th annual IMO Lecture to the Royal Society / 654 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $pi $ in base 2 / 663 Appendix I --- On the Early History of Pi / 677 Appendix II --- A Computational Chronology of Pi / 683 Appendix III --- Selected Formulae for Pi / 686 Bibliography / 690 Credits / 697 Index / 701

rawabstract:
The aim of this book is to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics, and a surprising amount of the most important mathematics and mathematicians have contributed to its unfolding. Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. Yet, despite this, no source book on pi has been published. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet still accessible, mathematics. Mathematicians and historians of mathematics will find this book indispensable. Teachers at every level from the seventh grade onward will find here ample resources for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: first a selection of the mathematical literature of four millennia, second a variety of historical studies or writings on the cultural meaning and significance of the number, and third, a number of treatments on pi that are fanciful, satirical and/or whimsical.

rawTOC:
Preface / v \\ \\ Acknowledgments / ix \\ \\ Introduction / xvii \\ \\ 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ \\ 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ \\ 3. Archimedes. Measurement of a Circle ($\approx$ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $\pi$ / 7 \\ \\ 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $\pi$ using modern notation / 15 \\ \\ 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $\pi$ and also examines values for $\pi$ given by Zu Chongzhi (429--500) / 20 \\ \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures ($\approx$ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ \\ 7. M{\=a}dhava. The Power Series for Arctan and Pi ($\approx$ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $\pi$ / 45 \\ \\ 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $\pi$ / 51 \\ \\ 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $\pi$, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ \\ 10. Wallis. Computation of $\pi$ by Successive Interpolations (1655) / How Wallis derived the infinite product for $\pi$ that bears his name / 68 \\ \\ 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/\pi$ / 78 \\ \\ 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 \\ \\ 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 \\ \\ 14. Roy. The Discovery of the Series Formula for $\pi$ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $\pi/4 = 1 - 1/3 + 1/5, \cdots{}$ / 92 \\ \\ 15. Jones. The First Use of $\pi$ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 \\ \\ 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $\pi$ to 16 decimal places / 110 \\ \\ 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $\pi$ and powers of $\pi$ / 112 \\ \\ 18. Lambert. M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $\pi$ / 129 \\ \\ 19. Lambert. Irrationality of $\pi$ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $\pi$ / 141 \\ \\ 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $\pi$ / 147 \\ \\ 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 \\ \\ 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first proof of the transcendence of $\pi$ / 194 \\ \\ 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $\pi$ / 207 \\ \\ 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $\pi$ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $\pi$ / 226 \\ \\ 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $\pi$ in Indiana / 230 \\ \\ 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $\pi$ (including a copy of the actual bill that was proposed) / 231 \\ \\ 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $\pi$ / 236 \\ \\ 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $\pi$ / 240 \\ \\ 29. Ramanujan. Modular Equations and Approximations to $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that includes a number of striking series and algebraic approximations / 241 \\ \\ 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 \\ \\ 31. Ballantine. The Best (?) Formula for Computing $\pi$ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $\pi$ more cleverly / 271 \\ \\ 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $\pi / 4 $ as a sum of arctan relations in powers of 10 / 274 \\ \\ 33. Niven. A Simple Proof that $\pi$ Is Irrational (1947) / A very concise proof of the irrationality of $\pi$ / 276 \\ \\ 34. Reitwiesner. An ENIAC Determination of $\pi$ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ \\ 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $\pi$ from 3000 BC to 1949 / 282 \\ \\ 36. Mahler. On the Approximation of $\pi$ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $\pi$ from a given rational or algebraic number'' / 306 \\ \\ 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $\pi$ (1960) / A history of the calculation of the digits of $\pi$ to 1960 \\ \\ 38. Shanks and Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals (1962) / A landmark computation of $\pi$ to more than 100,000 places / 326 \\ \\ 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 \\ \\ 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ \\ 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 \\ \\ 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 \\ \\ 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $\pi$ / 400 \\ \\ 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $\pi$ / 402 \\ \\ 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ \\ 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $\pi$ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ \\ 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 \\ \\ 48. Beukers. A Note on the Irrationality of $\zeta(2)$ and $\zetq(3)$ (1979) / A short and elegant recasting of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ \\ 49. van der Poorten. A Proof that Euler Missed \ldots{} Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$ (1979) / An illuminating account of Ap{\'e}ry's astonishing proof of the irrationality of $\zeta(3)$ / 439 \\ \\ 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ \\ 51. Apostol. A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi / 6$ / 456 \\ \\ 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ \\ 53. Stern. A Remarkable Approximation to $\pi$ (1985) / Justification of the value of $\pi$ in the Bible through numerological interpretations / 460 \\ \\ 54. Newman and Shanks. On a Sequence Arising in Series for $\pi$ (1984) / More connections between $\pi$ and modular equations / 462 \\ \\ 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ \\ 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $\pi$) / 537 \\ \\ 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $\pi$ using the Gauss AGM without explicit elliptic function theory / 553 \\ \\ 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $\pi$ has randomly distributed digits / 557 \\ \\ 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $\pi$ / 560 \\ \\ 60. Bailey. The Computation of $\pi$ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $\pi$ and for performing the required multiple-precision arithmetic / 562 \\ \\ 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $\pi$ / 576 \\ \\ 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $\pi$, and how his approach is now incorporated into modern computer algorithms / 588 \\ \\ 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $\pi$ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ \\ 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $\pi$ using mathematics rooted in Ramanujan's work / 623 \\ \\ 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $\pi$, truncated at 500,000 terms, gives $\pi$ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ \\ 66. Beukers, B{\'e}zivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ \\ 67. Webster. The Tail of Pi (1991) / Various anecdotes about $\pi$ from the 14th annual IMO Lecture to the Royal Society / 654 \\ \\ 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ \\ 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $\pi$ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ \\ 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $\pi$ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ \\ Appendix II --- A Computational Chronology of Pi / 683 \\ \\ Appendix III --- Selected Formulae for Pi / 686 \\ \\ Bibliography / 690 \\ \\ Credits / 697 \\ \\ Index / 701

entry:
@Book{Berggren:1997:PSB,
  editor =       "Lennart Berggren and Jonathan M. Borwein and Peter B.
                 Borwein",
  booktitle =    "Pi, a source book",
  title =        "Pi, a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 716",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4",
  ISBN =         "0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0
                 (print), 3-540-94924-0",
  ISBN-13 =      "978-0-387-94924-6, 978-1-4757-2736-4 (e-book),
                 978-1-4757-2738-8 (print), 978-3-540-94924-4",
  LCCN =         "QA484 .P5 1997",
  bibdate =      "Fri Sep 2 17:41:50 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "The aim of this book is to provide a complete history
                 of pi from the dawn of mathematical time to the
                 present. The story of pi reflects the most seminal, the
                 most serious and sometimes the silliest aspects of
                 mathematics, and a surprising amount of the most
                 important mathematics and mathematicians have
                 contributed to its unfolding. Pi is one of the few
                 concepts in mathematics whose mention evokes a response
                 of recognition and interest in those not concerned
                 professionally with the subject. Yet, despite this, no
                 source book on pi has been published. One of the
                 beauties of the literature on pi is that it allows for
                 the inclusion of very modern, yet still accessible,
                 mathematics. Mathematicians and historians of
                 mathematics will find this book indispensable. Teachers
                 at every level from the seventh grade onward will find
                 here ample resources for anything from special topic
                 courses to individual talks and special student
                 projects. The literature on pi included in this source
                 book falls into three classes: first a selection of the
                 mathematical literature of four millennia, second a
                 variety of historical studies or writings on the
                 cultural meaning and significance of the number, and
                 third, a number of treatments on pi that are fanciful,
                 satirical and/or whimsical.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi; Pi (Le nombre); Pi.; Pi (le nombre)",
  tableofcontents = "Preface / v \\
                 \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Bibliography / 690 \\
                 \\
                 Credits / 697 \\
                 \\
                 Index / 701",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Borwein:1997:OMP
editor: Jonathan M. Borwein and Peter B. Borwein and Loki Jorgenson and Rob Corless
volume: 20
publisher: pub-AMS
address: pub-AMS:adr
pages: ix + 412
year: 1997
ISBN: 0-8218-0668-8 OR 0821806688
ISBN13: 978-0-8218-0668-5 OR 9780821806685
ISSN: 0731-1036 OR 07311036
LCCN: QA1 .O67 1995
MRclass: 00B25 (11-06)
MRnumber: 1483910
bibdate: Tue Aug 16 08:57:59 MDT 2016
bibtimestamp: 2016.08.16 08:57:59 MDT
series: CMS conference proceedings
acknowledgement: ack-nhfb
raweditor: Jonathan M. Borwein and Peter B. Borwein and Loki J{\"o}rgenson and Rob Corless
ORCID: Borwein, Jonathan/0000-0002-1263-0646
booktitle:
Organic mathematics: proceedings of the Organic Mathematics Workshop, December 12--14, 1995, Simon Fraser University, Burnaby, British Columbia

title:
Organic mathematics: proceedings of the Organic Mathematics Workshop, December 12--14, 1995, Simon Fraser University, Burnaby, British Columbia

remark:
Am Kopf der Titelseite: Canadian Mathematical Society = Societe Mathematique du Canada. ``This volume is the ''hardcopy`` version of the intrinsically electronic ''Proceedings of the Organic Mathematics Workshop`` held ldots in December of 1995''. ``Published by the American Mathematical Society for the Canadian Mathematical Society''.

TOC:
Jonathan M. Borwein, Peter B. Borwein, Robert M. Corless, Loki Jorgenson and Nathalie Sinclair / What is organic mathematics? / 1--18 George E. Andrews / Pfaff's method. III. Comparison with the WZ method [MR1392506] / 19--34 D. H. Bailey, J. M. Borwein and P. B. Borwein / Ramanujan, modular equations, and approximations to pi or How to compute one billion digits of pi [MR0991866] / 35--71 David H. Bailey and Simon Plouffe / Recognizing numerical constants / 73--88 J. M. Borwein and F. G. Garvan / Approximations to $ pi $ via the Dedekind eta function / 89--115 David W. Boyd / The beta expansion for Salem numbers / 117--131 Joe Buhler, David Eisenbud, Ron Graham and Colin Wright [Colin Douglas Wright] / Juggling drops and descents [MR1274973] / 133--154 Arjeh M. Cohen and David B. Wales / GL(4)-orbits in a 16-dimensional module for characteristic 3 [MR1409976] / 155--174 K. Belabas and H. Cohen [Henri Cohen] / Binary cubic forms and cubic number fields / 175--204 Robert M. Corless / Continued fractions and chaos [MR1216205] / 205--238 P. J. Forrester and A. M. Odlyzko / A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices / 239--251 Andrew Granville / Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers / 253--276 John H. Hubbard, Jean Marie McDill, Anne Noonburg and Beverly H. West / A new look at the Airy equation with fences and funnels / 277--303 Jeffrey C. Lagarias / The $ 3 x + 1 $ problem and its generalizations [MR0777565] / 305--334 C. W. H. Lam / The search for a finite projective plane of order 10 [MR1103185] / 335--355 Stan Wagon / New visualization ideas for differential equations / 357--381 Selected images from the Proceedings / 383--386 Stephen P. Braham / Internet, executable content, and the future of mathematical science communication / 387--405 Wayne Haga and Sinai Robins / On Kruskal's principle / 407--412

rawbooktitle:
{Organic mathematics: proceedings of the Organic Mathematics Workshop, December 12--14, 1995, Simon Fraser University, Burnaby, British Columbia}

rawtitle:
{Organic mathematics: proceedings of the Organic Mathematics Workshop, December 12--14, 1995, Simon Fraser University, Burnaby, British Columbia}

rawTOC:
Jonathan M. Borwein, Peter B. Borwein, Robert M. Corless, Loki J{\"o}rgenson and Nathalie Sinclair / What is organic mathematics? / 1--18 \\ George E. Andrews / Pfaff's method. III. Comparison with the WZ method [MR1392506] / 19--34 \\ D. H. Bailey, J. M. Borwein and P. B. Borwein / Ramanujan, modular equations, and approximations to pi or How to compute one billion digits of pi [MR0991866] / 35--71 \\ David H. Bailey and Simon Plouffe / Recognizing numerical constants / 73--88 \\ J. M. Borwein and F. G. Garvan / Approximations to $ \pi $ via the Dedekind eta function / 89--115 \\ David W. Boyd / The beta expansion for Salem numbers / 117--131 \\ Joe Buhler, David Eisenbud, Ron Graham and Colin Wright [Colin Douglas Wright] / Juggling drops and descents [MR1274973] / 133--154 \\ Arjeh M. Cohen and David B. Wales / GL(4)-orbits in a 16-dimensional module for characteristic 3 [MR1409976] / 155--174 \\ K. Belabas and H. Cohen [Henri Cohen] / Binary cubic forms and cubic number fields / 175--204 \\ Robert M. Corless / Continued fractions and chaos [MR1216205] / 205--238 \\ P. J. Forrester and A. M. Odlyzko / A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices / 239--251 \\ Andrew Granville / Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers / 253--276 \\ John H. Hubbard, Jean Marie McDill, Anne Noonburg and Beverly H. West / A new look at the Airy equation with fences and funnels / 277--303 \\ Jeffrey C. Lagarias / The $ 3 x + 1 $ problem and its generalizations [MR0777565] / 305--334 \\ C. W. H. Lam / The search for a finite projective plane of order 10 [MR1103185] / 335--355 \\ Stan Wagon / New visualization ideas for differential equations / 357--381 \\ Selected images from the Proceedings / 383--386 \\ Stephen P. Braham / Internet, executable content, and the future of mathematical science communication / 387--405 \\ Wayne Haga and Sinai Robins / On Kruskal's principle / 407--412

entry:
@Proceedings{Borwein:1997:OMP,
  editor =       "Jonathan M. Borwein and Peter B. Borwein and Loki
                 J{\"o}rgenson and Rob Corless",
  booktitle =    "{Organic mathematics: proceedings of the Organic
                 Mathematics Workshop, December 12--14, 1995, Simon
                 Fraser University, Burnaby, British Columbia}",
  title =        "{Organic mathematics: proceedings of the Organic
                 Mathematics Workshop, December 12--14, 1995, Simon
                 Fraser University, Burnaby, British Columbia}",
  volume =       "20",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 412",
  year =         "1997",
  ISBN =         "0-8218-0668-8",
  ISBN-13 =      "978-0-8218-0668-5",
  ISSN =         "0731-1036",
  LCCN =         "QA1 .O67 1995",
  MRclass =      "00B25 (11-06)",
  MRnumber =     "1483910",
  bibdate =      "Tue Aug 16 08:57:59 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CMS conference proceedings",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Am Kopf der Titelseite: Canadian Mathematical Society
                 = Soci{\'e}t{\'e} Math{\'e}matique du Canada. ``This
                 volume is the ''hardcopy`` version of the intrinsically
                 electronic ''Proceedings of the Organic Mathematics
                 Workshop`` held \ldots{} in December of 1995''.
                 ``Published by the American Mathematical Society for
                 the Canadian Mathematical Society''.",
  tableofcontents = "Jonathan M. Borwein, Peter B. Borwein, Robert M.
                 Corless, Loki J{\"o}rgenson and Nathalie Sinclair /
                 What is organic mathematics? / 1--18 \\
                 George E. Andrews / Pfaff's method. III. Comparison
                 with the WZ method [MR1392506] / 19--34 \\
                 D. H. Bailey, J. M. Borwein and P. B. Borwein /
                 Ramanujan, modular equations, and approximations to pi
                 or How to compute one billion digits of pi [MR0991866]
                 / 35--71 \\
                 David H. Bailey and Simon Plouffe / Recognizing
                 numerical constants / 73--88 \\
                 J. M. Borwein and F. G. Garvan / Approximations to $
                 \pi $ via the Dedekind eta function / 89--115 \\
                 David W. Boyd / The beta expansion for Salem numbers /
                 117--131 \\
                 Joe Buhler, David Eisenbud, Ron Graham and Colin Wright
                 [Colin Douglas Wright] / Juggling drops and descents
                 [MR1274973] / 133--154 \\
                 Arjeh M. Cohen and David B. Wales / GL(4)-orbits in a
                 16-dimensional module for characteristic 3 [MR1409976]
                 / 155--174 \\
                 K. Belabas and H. Cohen [Henri Cohen] / Binary cubic
                 forms and cubic number fields / 175--204 \\
                 Robert M. Corless / Continued fractions and chaos
                 [MR1216205] / 205--238 \\
                 P. J. Forrester and A. M. Odlyzko / A nonlinear
                 equation and its application to nearest neighbor
                 spacings for zeros of the zeta function and eigenvalues
                 of random matrices / 239--251 \\
                 Andrew Granville / Arithmetic properties of binomial
                 coefficients. I. Binomial coefficients modulo prime
                 powers / 253--276 \\
                 John H. Hubbard, Jean Marie McDill, Anne Noonburg and
                 Beverly H. West / A new look at the Airy equation with
                 fences and funnels / 277--303 \\
                 Jeffrey C. Lagarias / The $ 3 x + 1 $ problem and its
                 generalizations [MR0777565] / 305--334 \\
                 C. W. H. Lam / The search for a finite projective plane
                 of order 10 [MR1103185] / 335--355 \\
                 Stan Wagon / New visualization ideas for differential
                 equations / 357--381 \\
                 Selected images from the Proceedings / 383--386 \\
                 Stephen P. Braham / Internet, executable content, and
                 the future of mathematical science communication /
                 387--405 \\
                 Wayne Haga and Sinai Robins / On Kruskal's principle /
                 407--412",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Berggren:2000:PSB
editor: Lennart Berggren and Jonathan Borwein and Peter Borwein
booktitle: Pi: a source book
title: Pi: a source book
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xx + 736
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-3240-5
ISBN: 0-387-98946-3 (hardcover) OR 0387989463 (hardcover)
ISBN13: 978-0-387-98946-4 (hardcover) OR 9780387989464 (hardcover)
LCCN: QA484 .P5 2000
MRclass: 11-00 (01A05 01A75 11-03)
MRnumber: 1746004
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
subject: Pi (mathematical constant)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawbooktitle: Pi: a source book
raweditor: Lennart Berggren and Jonathan Borwein and Peter Borwein
rawtitle: Pi: a source book
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

TOC:
Preface / v Preface to the Second Edition / viii Acknowledgments / ix Introduction / xvii 1. The Rhind Mathematical Papyrus-Problem 50 ($approx $ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 3. Archimedes. Measurement of a Circle ($approx $ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $pi $ / 7 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $pi $ using modern notation / 15 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $pi $ and also examines values for $pi $ given by Zu Chongzhi (429--500) / 20 6. The Banu Musa: The Measurement of Plane and Solid Figures ($approx $ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 7. Madhava. The Power Series for Arctan and Pi ($approx $ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $pi $ / 45 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $pi $ / 51 9. Viete. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 10. Wallis. Computation of $pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $pi $ that bears his name / 68 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/pi $ / 78 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 14. Roy. The Discovery of the Series Formula for $pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $pi /4 = 1 - 1/3 + 1/5, cdots $ / 92 15. Jones. The First Use of $pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $pi $ to 16 decimal places / 110 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $pi $ and powers of $pi $ / 112 18. Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $pi $ / 129 19. Lambert. Irrationality of $pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $pi $ / 141 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $pi $ / 147 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 22. Lindemann. Ueber die Zahl $pi $ (1882) / The first proof of the transcendence of $pi $ / 194 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $pi $ / 207 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $pi $ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $pi $ / 226 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $pi $ in Indiana / 230 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $pi $ (including a copy of the actual bill that was proposed) / 231 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $pi $ / 236 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $pi $ / 240 29. Ramanujan. Modular Equations and Approximations to $pi $ (1914) / Ramanujan's seminal paper on $pi $ that includes a number of striking series and algebraic approximations / 241 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 31. Ballantine. The Best (?) Formula for Computing $pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $pi $ more cleverly / 271 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $pi / 4 $ as a sum of arctan relations in powers of 10 / 274 33. Niven. A Simple Proof that $pi $ Is Irrational (1947) / A very concise proof of the irrationality of $pi $ / 276 34. Reitwiesner. An ENIAC Determination of $pi $ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $pi $ from 3000 BC to 1949 / 282 36. Mahler. On the Approximation of $pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $pi $ from a given rational or algebraic number'' / 306 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $pi $ (1960) / A history of the calculation of the digits of $pi $ to 1960 38. Shanks and Wrench, Jr. Calculation of $pi $ to 100,000 Decimals (1962) / A landmark computation of $pi $ to more than 100,000 places / 326 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $pi $ / 400 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $pi $ / 402 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 48. Beukers. A Note on the Irrationality of $zeta (2)$ and $zetq (3)$ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $zeta (3)$ (and $zeta (2)$) / 434 49. van der Poorten. A Proof that Euler Missed ldots Apery's Proof of the Irrationality of $zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $zeta (3)$ / 439 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 51. Apostol. A Proof that Euler Missed: Evaluating $zeta (2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $zeta (2) = pi / 6$ / 456 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 53. Stern. A Remarkable Approximation to $pi $ (1985) / Justification of the value of $pi $ in the Bible through numerological interpretations / 460 54. Newman and Shanks. On a Sequence Arising in Series for $pi $ (1984) / More connections between $pi $ and modular equations / 462 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $pi $) / 537 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $pi $ using the Gauss AGM without explicit elliptic function theory / 553 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $pi $ has randomly distributed digits / 557 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $pi $ / 560 60. Bailey. The Computation of $pi $ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $pi $ and for performing the required multiple-precision arithmetic / 562 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $pi $ / 576 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $pi $, and how his approach is now incorporated into modern computer algorithms / 588 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $pi $ using mathematics rooted in Ramanujan's work / 623 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $pi $, truncated at 500,000 terms, gives $pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 66. Beukers, Bezivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 67. Webster. The Tail of Pi (1991) / Various anecdotes about $pi $ from the 14th annual IMO Lecture to the Royal Society / 654 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $pi $ in base 2 / 663 Appendix I --- On the Early History of Pi / 677 Appendix II --- A Computational Chronology of Pi / 683 Appendix III --- Selected Formulae for Pi / 686 Appendix IV --- Translations of Viete and Huygens / 690 Bibliography / 711 Credits / 717 Index / 721

rawTOC:
Preface / v \\ \\ Preface to the Second Edition / viii \\ Acknowledgments / ix \\ \\ Introduction / xvii \\ \\ 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ \\ 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ \\ 3. Archimedes. Measurement of a Circle ($\approx$ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $\pi$ / 7 \\ \\ 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $\pi$ using modern notation / 15 \\ \\ 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $\pi$ and also examines values for $\pi$ given by Zu Chongzhi (429--500) / 20 \\ \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures ($\approx$ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ \\ 7. M{\=a}dhava. The Power Series for Arctan and Pi ($\approx$ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $\pi$ / 45 \\ \\ 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $\pi$ / 51 \\ \\ 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $\pi$, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ \\ 10. Wallis. Computation of $\pi$ by Successive Interpolations (1655) / How Wallis derived the infinite product for $\pi$ that bears his name / 68 \\ \\ 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/\pi$ / 78 \\ \\ 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 \\ \\ 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 \\ \\ 14. Roy. The Discovery of the Series Formula for $\pi$ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $\pi/4 = 1 - 1/3 + 1/5, \cdots{}$ / 92 \\ \\ 15. Jones. The First Use of $\pi$ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 \\ \\ 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $\pi$ to 16 decimal places / 110 \\ \\ 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $\pi$ and powers of $\pi$ / 112 \\ \\ 18. Lambert. M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $\pi$ / 129 \\ \\ 19. Lambert. Irrationality of $\pi$ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $\pi$ / 141 \\ \\ 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $\pi$ / 147 \\ \\ 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 \\ \\ 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first proof of the transcendence of $\pi$ / 194 \\ \\ 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $\pi$ / 207 \\ \\ 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $\pi$ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $\pi$ / 226 \\ \\ 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $\pi$ in Indiana / 230 \\ \\ 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $\pi$ (including a copy of the actual bill that was proposed) / 231 \\ \\ 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $\pi$ / 236 \\ \\ 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $\pi$ / 240 \\ \\ 29. Ramanujan. Modular Equations and Approximations to $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that includes a number of striking series and algebraic approximations / 241 \\ \\ 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 \\ \\ 31. Ballantine. The Best (?) Formula for Computing $\pi$ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $\pi$ more cleverly / 271 \\ \\ 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $\pi / 4 $ as a sum of arctan relations in powers of 10 / 274 \\ \\ 33. Niven. A Simple Proof that $\pi$ Is Irrational (1947) / A very concise proof of the irrationality of $\pi$ / 276 \\ \\ 34. Reitwiesner. An ENIAC Determination of $\pi$ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ \\ 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $\pi$ from 3000 BC to 1949 / 282 \\ \\ 36. Mahler. On the Approximation of $\pi$ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $\pi$ from a given rational or algebraic number'' / 306 \\ \\ 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $\pi$ (1960) / A history of the calculation of the digits of $\pi$ to 1960 \\ \\ 38. Shanks and Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals (1962) / A landmark computation of $\pi$ to more than 100,000 places / 326 \\ \\ 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 \\ \\ 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ \\ 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 \\ \\ 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 \\ \\ 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $\pi$ / 400 \\ \\ 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $\pi$ / 402 \\ \\ 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ \\ 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $\pi$ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ \\ 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 \\ \\ 48. Beukers. A Note on the Irrationality of $\zeta(2)$ and $\zetq(3)$ (1979) / A short and elegant recasting of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ \\ 49. van der Poorten. A Proof that Euler Missed \ldots{} Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$ (1979) / An illuminating account of Ap{\'e}ry's astonishing proof of the irrationality of $\zeta(3)$ / 439 \\ \\ 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ \\ 51. Apostol. A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi / 6$ / 456 \\ \\ 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ \\ 53. Stern. A Remarkable Approximation to $\pi$ (1985) / Justification of the value of $\pi$ in the Bible through numerological interpretations / 460 \\ \\ 54. Newman and Shanks. On a Sequence Arising in Series for $\pi$ (1984) / More connections between $\pi$ and modular equations / 462 \\ \\ 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ \\ 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $\pi$) / 537 \\ \\ 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $\pi$ using the Gauss AGM without explicit elliptic function theory / 553 \\ \\ 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $\pi$ has randomly distributed digits / 557 \\ \\ 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $\pi$ / 560 \\ \\ 60. Bailey. The Computation of $\pi$ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $\pi$ and for performing the required multiple-precision arithmetic / 562 \\ \\ 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $\pi$ / 576 \\ \\ 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $\pi$, and how his approach is now incorporated into modern computer algorithms / 588 \\ \\ 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $\pi$ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ \\ 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $\pi$ using mathematics rooted in Ramanujan's work / 623 \\ \\ 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $\pi$, truncated at 500,000 terms, gives $\pi$ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ \\ 66. Beukers, B{\'e}zivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ \\ 67. Webster. The Tail of Pi (1991) / Various anecdotes about $\pi$ from the 14th annual IMO Lecture to the Royal Society / 654 \\ \\ 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ \\ 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $\pi$ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ \\ 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $\pi$ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ \\ Appendix II --- A Computational Chronology of Pi / 683 \\ \\ Appendix III --- Selected Formulae for Pi / 686 \\ \\ Appendix IV --- Translations of Vi{\`e}te and Huygens / 690 \\ Bibliography / 711 \\ \\ Credits / 717 \\ \\ Index / 721

entry:
@Book{Berggren:2000:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 736",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5",
  ISBN =         "0-387-98946-3 (hardcover)",
  ISBN-13 =      "978-0-387-98946-4 (hardcover)",
  LCCN =         "QA484 .P5 2000",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "1746004",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  libnote =      "Not yet in my library.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi (mathematical constant)",
  tableofcontents = "Preface / v \\
                 \\
                 Preface to the Second Edition / viii \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Appendix IV --- Translations of Vi{\`e}te and Huygens /
                 690 \\
                 Bibliography / 711 \\
                 \\
                 Credits / 717 \\
                 \\
                 Index / 721",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Berndt:2001:RES
editor: Bruce C. Berndt and Robert A. (Robert Alexander) Rankin
booktitle: Ramanujan: essays and surveys
title: Ramanujan: essays and surveys
volume: 22
publisher: pub-AMS
address: pub-AMS:adr
pages: xvi + 347
year: 2001
ISBN: 0-8218-2624-7 OR 0821826247
ISBN13: 978-0-8218-2624-9 OR 9780821826249
ISSN: 0899-2428 OR 08992428
ISSNL: 0899-2428 OR 08992428
LCCN: QA29.R3 R29 2001
MRnumber: 11-03, 01A70, 00B60, 01-06
bibdate: Sat Sep 3 16:48:18 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.09.03 16:48:18 MDT
series: History of mathematics
subject: Ramanujan Aiyangar, Srinivasa; Mathematicians; India; Biography; Number theory
ZMnumber: 1117.11002
acknowledgement: ack-nhfb
subjectdates: 1887--1920
rawbooktitle: {Ramanujan}: essays and surveys
raweditor: Bruce C. Berndt and Robert A. (Robert Alexander) Rankin
rawtitle: {Ramanujan}: essays and surveys
TOC:
Bruce C. Berndt / The four photographs of Ramanujan / 3--8 Bruce C. Berndt and Robert A. Rankin / The books studied by Ramanujan in India / 9--15 Bruce C. Berndt / The influence of Carr's synopsis on Ramanujan / 17--20 Bruce C. Berndt / The notebooks of Srinivasa Ramanujan / 21--22 A recently discovered letter giving Ramanujan's examination scores / 23 S. Chandrasekhar / On Ramanujan / 25--27 Robert A. Rankin / The Ramanujan family record / 29--38 R. A. Rankin / Ramanujan as a patient / 41--64 D. A. B. Young / Ramanujan's illness / 65--75 S. Chandrasekhar / An incident in the life of S. Ramanujan, F.R.S.: conversations with G. H. Hardy, F.R.S. and J. E. Littlewood, F.R.S. and their sequel / 77--79 Bruce C. Berndt / S. Janaki Ammal (Mrs. Ramanujan) / 83--87 Pritish Nandy / Conversation: ``I didn't understand his work, but I knew his worth'' / 89--93 Bruce C. Berndt / A short biography of S. Narayana Iyer / 97--98 S. Narayana Aiyar / The distribution of primes / 99--100 S. Narayana Aiyar / Some theorems in summation / 101--103 E. H. Neville / Srinivasa Ramanujan / 107--112 University lectures in Madras / 113 R. A. Rankin / Ramanujan's manuscripts and notebooks / 117--128 R. A. Rankin / Ramanujan's manuscripts and notebooks. II / 129--142 Bruce C. Berndt / An overview of Ramanujan's notebooks / 143--164 George E. Andrews / An introduction to Ramanujan's ``lost'' notebook / 165--184 Jonathan M. Borwein and Peter B. Borwein / Ramanujan and pi / 187--199 Bruce C. Berndt / $pi $ related developments since 1988 / 201 Atle Selberg / Reflections around the Ramanujan centenary / 203--213 Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang / The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society / 215--258 Freeman J. Dyson / A walk through Ramanujan's garden / 261--275 R. Askey / Ramanujan and hypergeometric and basic hypergeometric series / 277--324 G. N. Watson / The final problem: an account of the mock theta functions / 325--347

rawTOC:
Bruce C. Berndt / The four photographs of Ramanujan / 3--8 \\ Bruce C. Berndt and Robert A. Rankin / The books studied by Ramanujan in India / 9--15 \\ Bruce C. Berndt / The influence of Carr's synopsis on Ramanujan / 17--20 \\ Bruce C. Berndt / The notebooks of Srinivasa Ramanujan / 21--22 \\ A recently discovered letter giving Ramanujan's examination scores / 23 \\ S. Chandrasekhar / On Ramanujan / 25--27 \\ Robert A. Rankin / The Ramanujan family record / 29--38 \\ R. A. Rankin / Ramanujan as a patient / 41--64 \\ D. A. B. Young / Ramanujan's illness / 65--75 \\ S. Chandrasekhar / An incident in the life of S. Ramanujan, F.R.S.: conversations with G. H. Hardy, F.R.S. and J. E. Littlewood, F.R.S. and their sequel / 77--79 \\ Bruce C. Berndt / S. Janaki Ammal (Mrs. Ramanujan) / 83--87 \\ Pritish Nandy / Conversation: ``I didn't understand his work, but I knew his worth'' / 89--93 \\ Bruce C. Berndt / A short biography of S. Narayana Iyer / 97--98 \\ S. Narayana Aiyar / The distribution of primes / 99--100 \\ S. Narayana Aiyar / Some theorems in summation / 101--103 \\ E. H. Neville / Srinivasa Ramanujan / 107--112 \\ University lectures in Madras / 113 \\ R. A. Rankin / Ramanujan's manuscripts and notebooks / 117--128 \\ R. A. Rankin / Ramanujan's manuscripts and notebooks. II / 129--142 \\ Bruce C. Berndt / An overview of Ramanujan's notebooks / 143--164 \\ George E. Andrews / An introduction to Ramanujan's ``lost'' notebook / 165--184 \\ Jonathan M. Borwein and Peter B. Borwein / Ramanujan and pi / 187--199 \\ Bruce C. Berndt / $\pi$ related developments since 1988 / 201 \\ Atle Selberg / Reflections around the Ramanujan centenary / 203--213 \\ Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang / The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society / 215--258 \\ Freeman J. Dyson / A walk through Ramanujan's garden / 261--275 \\ R. Askey / Ramanujan and hypergeometric and basic hypergeometric series / 277--324 \\ G. N. Watson / The final problem: an account of the mock theta functions / 325--347

entry:
@Book{Berndt:2001:RES,
  editor =       "Bruce C. Berndt and Robert A. (Robert Alexander)
                 Rankin",
  booktitle =    "{Ramanujan}: essays and surveys",
  title =        "{Ramanujan}: essays and surveys",
  volume =       "22",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xvi + 347",
  year =         "2001",
  ISBN =         "0-8218-2624-7",
  ISBN-13 =      "978-0-8218-2624-9",
  ISSN =         "0899-2428",
  ISSN-L =       "0899-2428",
  LCCN =         "QA29.R3 R29 2001",
  MRnumber =     "11-03, 01A70, 00B60, 01-06",
  bibdate =      "Sat Sep 3 16:48:18 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "History of mathematics",
  ZMnumber =     "1117.11002",
  acknowledgement = ack-nhfb,
  subject =      "Ramanujan Aiyangar, Srinivasa; Mathematicians; India;
                 Biography; Number theory",
  subject-dates = "1887--1920",
  tableofcontents = "Bruce C. Berndt / The four photographs of Ramanujan
                 / 3--8 \\
                 Bruce C. Berndt and Robert A. Rankin / The books
                 studied by Ramanujan in India / 9--15 \\
                 Bruce C. Berndt / The influence of Carr's synopsis on
                 Ramanujan / 17--20 \\
                 Bruce C. Berndt / The notebooks of Srinivasa Ramanujan
                 / 21--22 \\
                 A recently discovered letter giving Ramanujan's
                 examination scores / 23 \\
                 S. Chandrasekhar / On Ramanujan / 25--27 \\
                 Robert A. Rankin / The Ramanujan family record / 29--38
                 \\
                 R. A. Rankin / Ramanujan as a patient / 41--64 \\
                 D. A. B. Young / Ramanujan's illness / 65--75 \\
                 S. Chandrasekhar / An incident in the life of S.
                 Ramanujan, F.R.S.: conversations with G. H. Hardy,
                 F.R.S. and J. E. Littlewood, F.R.S. and their sequel /
                 77--79 \\
                 Bruce C. Berndt / S. Janaki Ammal (Mrs. Ramanujan) /
                 83--87 \\
                 Pritish Nandy / Conversation: ``I didn't understand his
                 work, but I knew his worth'' / 89--93 \\
                 Bruce C. Berndt / A short biography of S. Narayana Iyer
                 / 97--98 \\
                 S. Narayana Aiyar / The distribution of primes /
                 99--100 \\
                 S. Narayana Aiyar / Some theorems in summation /
                 101--103 \\
                 E. H. Neville / Srinivasa Ramanujan / 107--112 \\
                 University lectures in Madras / 113 \\
                 R. A. Rankin / Ramanujan's manuscripts and notebooks /
                 117--128 \\
                 R. A. Rankin / Ramanujan's manuscripts and notebooks.
                 II / 129--142 \\
                 Bruce C. Berndt / An overview of Ramanujan's notebooks
                 / 143--164 \\
                 George E. Andrews / An introduction to Ramanujan's
                 ``lost'' notebook / 165--184 \\
                 Jonathan M. Borwein and Peter B. Borwein / Ramanujan
                 and pi / 187--199 \\
                 Bruce C. Berndt / $\pi$ related developments since 1988
                 / 201 \\
                 Atle Selberg / Reflections around the Ramanujan
                 centenary / 203--213 \\
                 Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang / The
                 problems submitted by Ramanujan to the Journal of the
                 Indian Mathematical Society / 215--258 \\
                 Freeman J. Dyson / A walk through Ramanujan's garden /
                 261--275 \\
                 R. Askey / Ramanujan and hypergeometric and basic
                 hypergeometric series / 277--324 \\
                 G. N. Watson / The final problem: an account of the
                 mock theta functions / 325--347",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Engquist:2001:MUB
editor: Bjorn Engquist and Wilfried Schmid
booktitle: Mathematics unlimited: 2001 and beyond
title: Mathematics unlimited: 2001 and beyond
publisher: pub-SV
address: pub-SV:adr
pages: xv + 1237
year: 2001
ISBN: 3-540-66913-2 OR 3540669132
ISBN13: 978-3-540-66913-5 OR 9783540669135
LCCN: QA7 .M32423 2001
bibdate: Mon Oct 31 14:18:00 MST 2005
bibtimestamp: 2005.10.31 14:18:00 MST
subject: Mathematics; Science; Mathematiques; Sciences
acknowledgement: ack-nhfb
rawbooktitle: Mathematics unlimited: 2001 and beyond
raweditor: Bj{\"o}rn Engquist and Wilfried Schmid
rawtitle: Mathematics unlimited: 2001 and beyond
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; melvyl.cdlib.org:210/CDL90

TOC:
Nonlinear Continuum Physics / Stuart S. Antman Computational Mechanics: Where Is It Going? / Ivo Babuska and J. Tinsley Oden From Finite Sets to Feynman Diagrams / John C. Baez and James Dolan Experimental Mathematics: Recent Developments and Future Outlook / David H. Bailey and Jonathan M. Borwein Mathematical Aspects of Econometrics / Badi H. Baltagi Quantum Information / Ole E. Barndorff-Nielsen, Richard D. Gill and Peter E. Jupp $p$-Adic $L$-Functions of Modular Elliptic Curves / Massimo Bertolini and Henri Darmon Basis for a New Relationship Between Mathematics and Society / Jean-Pierre Bourguignon New Issues in the Mathematics of Control / Roger Brockett

rawTOC:
Nonlinear Continuum Physics / Stuart S. Antman \\ Computational Mechanics: Where Is It Going? / Ivo Babu{\v{s}}ka and J. Tinsley Oden \\ From Finite Sets to Feynman Diagrams / John C. Baez and James Dolan \\ Experimental Mathematics: Recent Developments and Future Outlook / David H. Bailey and Jonathan M. Borwein \\ Mathematical Aspects of Econometrics / Badi H. Baltagi \\ Quantum Information / Ole E. Barndorff-Nielsen, Richard D. Gill and Peter E. Jupp \\ $p$-Adic $L$-Functions of Modular Elliptic Curves / Massimo Bertolini and Henri Darmon \\ Basis for a New Relationship Between Mathematics and Society / Jean-Pierre Bourguignon \\ New Issues in the Mathematics of Control / Roger Brockett

entry:
@Book{Engquist:2001:MUB,
  editor =       "Bj{\"o}rn Engquist and Wilfried Schmid",
  booktitle =    "Mathematics unlimited: 2001 and beyond",
  title =        "Mathematics unlimited: 2001 and beyond",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 1237",
  year =         "2001",
  ISBN =         "3-540-66913-2",
  ISBN-13 =      "978-3-540-66913-5",
  LCCN =         "QA7 .M32423 2001",
  bibdate =      "Mon Oct 31 14:18:00 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  subject =      "Mathematics; Science; Math\'ematiques; Sciences",
  tableofcontents = "Nonlinear Continuum Physics / Stuart S. Antman \\
                 Computational Mechanics: Where Is It Going? / Ivo
                 Babu{\v{s}}ka and J. Tinsley Oden \\
                 From Finite Sets to Feynman Diagrams / John C. Baez and
                 James Dolan \\
                 Experimental Mathematics: Recent Developments and
                 Future Outlook / David H. Bailey and Jonathan M.
                 Borwein \\
                 Mathematical Aspects of Econometrics / Badi H. Baltagi
                 \\
                 Quantum Information / Ole E. Barndorff-Nielsen, Richard
                 D. Gill and Peter E. Jupp \\
                 $p$-Adic $L$-Functions of Modular Elliptic Curves /
                 Massimo Bertolini and Henri Darmon \\
                 Basis for a New Relationship Between Mathematics and
                 Society / Jean-Pierre Bourguignon \\
                 New Issues in the Mathematics of Control / Roger
                 Brockett",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Borwein:2002:MTC
editor: Jonathan M. Borwein and Maridee Morales and Konrad Polthier and Jose Francisco Rodrigues
booktitle: Multimedia Tools for Communicating Mathematics
title: Multimedia Tools for Communicating Mathematics
volume: 8
publisher: pub-SV
address: pub-SV:adr
pages: viii + 314
year: 2002
DOI: https://doi.org/10.1007/978-3-642-56240-2
ISBN: 3-540-42450-4 (hardcover) OR 3540424504 (hardcover)
ISBN13: 978-3-540-42450-5 (hardcover) OR 9783540424505 (hardcover)
LCCN: QA20.C65 M85 2002
bibdate: Tue Aug 16 08:52:06 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.08.16 08:52:06 MDT
series: Mathematics and visualization
subject: Mathematics; Computer-assisted instruction; Interactive multimedia
acknowledgement: ack-nhfb
rawbooktitle: Multimedia Tools for Communicating Mathematics
raweditor: Jonathan M. Borwein and Maridee Morales and Konrad Polthier and Jose Francisco Rodrigues
rawtitle: Multimedia Tools for Communicating Mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://www.loc.gov/catdir/enhancements/fy0817/2002283245-d.html; http://www.loc.gov/catdir/toc/fy032/2002283245.html

abstract:
This book on multimedia tools for communicating mathematics arose from presentations at an international workshop organized by the Centro de Matematica e Aplicacoes Fundamentais at the University of Lisbon, in November 2000, with the collaboration of the Sonderforschungsbereich 288 at the University of Technology in Berlin, and of the Centre for Experimental and Constructive Mathematics at Simon Fraser University in Burnaby, Canada. The MTCM2000 meeting aimed at the scientific methods and algorithms at work inside multimedia tools, and it provided an overview of the range of present multimedia projects, of their limitations and the underlying mathematical problems. This book presents some of the tools and algorithms currently being used to create new ways of making enhanced interactive presentations and multimedia courses. It is an invaluable and up-to-date reference book on multimedia tools presently available for mathematics and related subjects.

TOC:
Front Matter / i--viii 1: Computer animated mathematics videotapes / Tom M. Apostol / 1--27 2: Virtual reconstruction of a virtual exhibit / Thomas F. Banchoff and Davide P. Cervone / 29--38 3: An intuitive approach to elementary mathematics on the Web / Bruce Bauslaugh [and others] / 39--49 4: em OpenMath technology for interactive mathematical documents / Olga Caprotti, Arjeh M. Cohen, Hans Cuypers, Hans Sterk / 51--65 5: The StageTools package for creating geometry for the Web / Davide P. Cervone / 67--77 6: Communicating and learning mathematics and hypervideo / Teresa Chambel and Numo Guimaraes / 79--91 7: Collaboration in a multimedia laboratory / Eliane Cousquer / 93--116 8: jDvi, a way to put interactive TeX on the Web / Tim Hoffmann / 117--130 9: Visual calculus, development and tools / Lawrence S. Husch / 131--163 Color Plates / 141 10: EG-models --- a new journal for digital geometry models / Michael Joswig and Konrad Polthier / 165--190 11: Future of mathematical software / Ulrich H. Kortenkamp / 191--201 12: Dynamic setup for elementary geometry / Ulrich H. Kortenkamp and Jurgen Richter-Gebert / 203--219 13: Dynamic geometry on WWW / Gilles Kuntz / 221--229 14: Minimalistic tools for mathematical multimedia / Erich Neuwirth / 231--239 15: Publication of interactive visualizations and Java View / Konrad Polthier [and others] / 241--264 16: Solver learning environment for solving mathematical word problems: Pupils Discussions / Heli Ruokamo / 265--276 17: Interactive knot theory with KnotPlot / Robert G. Scharein and Kellogg S. Booth / 277--290 18: Developing Gato and CATBox with Python: Teaching Graph Algorithms through Visualization and Experimentation / Alexander Schliep and Winfried Hochstattler / 291--309 19: Rescalable real-time interactive computer animations / John M. Sullivan / 311--214

rawabstract:
This book on multimedia tools for communicating mathematics arose from presentations at an international workshop organized by the Centro de Matem{\'a}tica e Aplica{\c{c}}oes Fundamentais at the University of Lisbon, in November 2000, with the collaboration of the Sonderforschungsbereich 288 at the University of Technology in Berlin, and of the Centre for Experimental and Constructive Mathematics at Simon Fraser University in Burnaby, Canada. The MTCM2000 meeting aimed at the scientific methods and algorithms at work inside multimedia tools, and it provided an overview of the range of present multimedia projects, of their limitations and the underlying mathematical problems. This book presents some of the tools and algorithms currently being used to create new ways of making enhanced interactive presentations and multimedia courses. It is an invaluable and up-to-date reference book on multimedia tools presently available for mathematics and related subjects.

rawTOC:
Front Matter / i--viii \\ 1: Computer animated mathematics videotapes / Tom M. Apostol / 1--27 \\ 2: Virtual reconstruction of a virtual exhibit / Thomas F. Banchoff and Davide P. Cervone / 29--38 \\ 3: An intuitive approach to elementary mathematics on the Web / Bruce Bauslaugh [and others] / 39--49 \\ 4: {\em OpenMath\/} technology for interactive mathematical documents / Olga Caprotti, Arjeh M. Cohen, Hans Cuypers, Hans Sterk / 51--65 \\ 5: The StageTools package for creating geometry for the Web / Davide P. Cervone / 67--77 \\ 6: Communicating and learning mathematics and hypervideo / Teresa Chambel and Numo Guimar{\'a}es / 79--91 \\ 7: Collaboration in a multimedia laboratory / {\'E}liane Cousquer / 93--116 \\ 8: jDvi, a way to put interactive {\TeX} on the Web / Tim Hoffmann / 117--130 \\ 9: Visual calculus, development and tools / Lawrence S. Husch / 131--163 \\ Color Plates / 141 \\ 10: EG-models --- a new journal for digital geometry models / Michael Joswig and Konrad Polthier / 165--190 \\ 11: Future of mathematical software / Ulrich H. Kortenkamp / 191--201 \\ 12: Dynamic setup for elementary geometry / Ulrich H. Kortenkamp and J{\"u}rgen Richter-Gebert / 203--219 \\ 13: Dynamic geometry on WWW / Gilles Kuntz / 221--229 \\ 14: Minimalistic tools for mathematical multimedia / Erich Neuwirth / 231--239 \\ 15: Publication of interactive visualizations and Java View / Konrad Polthier [and others] / 241--264 \\ 16: Solver learning environment for solving mathematical word problems: Pupils Discussions / Heli Ruokamo / 265--276 \\ 17: Interactive knot theory with KnotPlot / Robert G. Scharein and Kellogg S. Booth / 277--290 \\ 18: Developing Gato and CATBox with Python: Teaching Graph Algorithms through Visualization and Experimentation / Alexander Schliep and Winfried Hochst{\"a}ttler / 291--309 \\ 19: Rescalable real-time interactive computer animations / John M. Sullivan / 311--214

entry:
@Proceedings{Borwein:2002:MTC,
  editor =       "Jonathan M. Borwein and Maridee Morales and Konrad
                 Polthier and Jose Francisco Rodrigues",
  booktitle =    "Multimedia Tools for Communicating Mathematics",
  title =        "Multimedia Tools for Communicating Mathematics",
  volume =       "8",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 314",
  year =         "2002",
  DOI =          "https://doi.org/10.1007/978-3-642-56240-2",
  ISBN =         "3-540-42450-4 (hardcover)",
  ISBN-13 =      "978-3-540-42450-5 (hardcover)",
  LCCN =         "QA20.C65 M85 2002",
  bibdate =      "Tue Aug 16 08:52:06 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics and visualization",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0817/2002283245-d.html;
                 http://www.loc.gov/catdir/toc/fy032/2002283245.html",
  abstract =     "This book on multimedia tools for communicating
                 mathematics arose from presentations at an
                 international workshop organized by the Centro de
                 Matem{\'a}tica e Aplica{\c{c}}oes Fundamentais at the
                 University of Lisbon, in November 2000, with the
                 collaboration of the Sonderforschungsbereich 288 at the
                 University of Technology in Berlin, and of the Centre
                 for Experimental and Constructive Mathematics at Simon
                 Fraser University in Burnaby, Canada. The MTCM2000
                 meeting aimed at the scientific methods and algorithms
                 at work inside multimedia tools, and it provided an
                 overview of the range of present multimedia projects,
                 of their limitations and the underlying mathematical
                 problems. This book presents some of the tools and
                 algorithms currently being used to create new ways of
                 making enhanced interactive presentations and
                 multimedia courses. It is an invaluable and up-to-date
                 reference book on multimedia tools presently available
                 for mathematics and related subjects.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Mathematics; Computer-assisted instruction;
                 Interactive multimedia",
  tableofcontents = "Front Matter / i--viii \\
                 1: Computer animated mathematics videotapes / Tom M.
                 Apostol / 1--27 \\
                 2: Virtual reconstruction of a virtual exhibit / Thomas
                 F. Banchoff and Davide P. Cervone / 29--38 \\
                 3: An intuitive approach to elementary mathematics on
                 the Web / Bruce Bauslaugh [and others] / 39--49 \\
                 4: {\em OpenMath\/} technology for interactive
                 mathematical documents / Olga Caprotti, Arjeh M. Cohen,
                 Hans Cuypers, Hans Sterk / 51--65 \\
                 5: The StageTools package for creating geometry for the
                 Web / Davide P. Cervone / 67--77 \\
                 6: Communicating and learning mathematics and
                 hypervideo / Teresa Chambel and Numo Guimar{\'a}es /
                 79--91 \\
                 7: Collaboration in a multimedia laboratory /
                 {\'E}liane Cousquer / 93--116 \\
                 8: jDvi, a way to put interactive {\TeX} on the Web /
                 Tim Hoffmann / 117--130 \\
                 9: Visual calculus, development and tools / Lawrence S.
                 Husch / 131--163 \\
                 Color Plates / 141 \\
                 10: EG-models --- a new journal for digital geometry
                 models / Michael Joswig and Konrad Polthier / 165--190
                 \\
                 11: Future of mathematical software / Ulrich H.
                 Kortenkamp / 191--201 \\
                 12: Dynamic setup for elementary geometry / Ulrich H.
                 Kortenkamp and J{\"u}rgen Richter-Gebert / 203--219 \\
                 13: Dynamic geometry on WWW / Gilles Kuntz / 221--229
                 \\
                 14: Minimalistic tools for mathematical multimedia /
                 Erich Neuwirth / 231--239 \\
                 15: Publication of interactive visualizations and Java
                 View / Konrad Polthier [and others] / 241--264 \\
                 16: Solver learning environment for solving
                 mathematical word problems: Pupils Discussions / Heli
                 Ruokamo / 265--276 \\
                 17: Interactive knot theory with KnotPlot / Robert G.
                 Scharein and Kellogg S. Booth / 277--290 \\
                 18: Developing Gato and CATBox with Python: Teaching
                 Graph Algorithms through Visualization and
                 Experimentation / Alexander Schliep and Winfried
                 Hochst{\"a}ttler / 291--309 \\
                 19: Rescalable real-time interactive computer
                 animations / John M. Sullivan / 311--214",
}


bibtype: proceedings
filename: borwein-jonathan-m.bib
label: Asperti:2003:MKM
editor: Andrea Asperti and Bruno Buchberger and James Harold Davenport
volume: 2594
publisher: pub-SV
address: pub-SV:adr
pages: x + 223
year: 2003
DOI: https://doi.org/10.1007/3540364692
ISBN: 3-540-00568-4 (softcover) OR 3540005684 (softcover)
ISBN13: 978-3-540-00568-1 (softcover) OR 9783540005681 (softcover)
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
LCCN: QA76.95 .I565 2003
bibdate: Sat Aug 13 17:26:10 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.08.13 17:26:10 MDT
series: Lecture notes in computer science
URL: http://www.loc.gov/catdir/enhancements/fy0817/2003042408-d.html
acknowledgement: ack-nhfb
raweditor: Andrea Asperti and Bruno Buchberger and James Harold Davenport
booktitle:
Mathematical knowledge management: second international conference, MKM 2003, Bertinoro, Italy, February 16--18, 2003: proceedings

title:
Mathematical knowledge management: second international conference, MKM 2003, Bertinoro, Italy, February 16--18, 2003: proceedings

subject:
Mathematics; Data processing; Congresses; Information storage and retrieval systems; Automatic theorem proving

TOC:
Digitisation, Representation, and Formalisation (Digital Libraries of Mathematics) / Andrew A. Adams / 1 MKM from Book to Computer: A Case Study / James H. Davenport / 17 From Proof-Assistants to Distributed Libraries of Mathematics: Tips and Pitfalls / Claudio Sacerdoti Coen / 30 Managing Digital Mathematical Discourse / Jonathan Borwein and Terry Stanway / 45 NAG Library Documentation / David Carlisle and Mike Dewar / 56 On the Roles of LaTeX and MathML in Encoding and Processing Mathematical Expressions / Luca Padovani / 66 Problems and Solutions for Markup for Mathematical Examples and Exercises / Georgi Goguadze, Erica Melis, Carsten Ullrich and Paul Cairns / 80 An Annotated Corpus and a Grammar Model of Theorem Description / Yusuke Baba and Masakazu Suzuki / 93 A Query Language for a Metadata Framework about Mathematical Resources / Ferruccio Guidi and Irene Schena / 105 Information Retrieval in MML / Grzegorz Bancerek and Piotr Rudnicki / 119 An Expert System for the Flexible Processing of XML-Based Mathematical Knowledge in a PROLOG-Environment / Bernd D. Heumesser, Dietmar A. Seipel and Ulrich Guntzer / 133 Towards Collaborative Content Management and Version Control for Structured Mathematical Knowledge / Michael Kohlhase and Romeo Anghelache / 147 On the Integrity of a Repository of Formalized Mathematics / Piotr Rudnicki and Andrzej Trybulec / 162 A Theoretical Analysis of Hierarchical Proofs / Paul Cairns and Jeremy Gow / 175 Comparing Mathematical Provers / Freek Wiedijk / 188 Translating Mizar for First Order Theorem Provers / Josef Urban / 203 The Mathematical Semantic Web / Massimo Marchiori / 216 Author Index / 225

rawbooktitle:
{Mathematical knowledge management: second international conference, MKM 2003, Bertinoro, Italy, February 16--18, 2003: proceedings}

rawtitle:
{Mathematical knowledge management: second international conference, MKM 2003, Bertinoro, Italy, February 16--18, 2003: proceedings}

rawTOC:
Digitisation, Representation, and Formalisation (Digital Libraries of Mathematics) / Andrew A. Adams / 1 \\ MKM from Book to Computer: A Case Study / James H. Davenport / 17 \\ From Proof-Assistants to Distributed Libraries of Mathematics: Tips and Pitfalls / Claudio Sacerdoti Coen / 30 \\ Managing Digital Mathematical Discourse / Jonathan Borwein and Terry Stanway / 45 \\ NAG Library Documentation / David Carlisle and Mike Dewar / 56 \\ On the Roles of \LaTeX{} and MathML in Encoding and Processing Mathematical Expressions / Luca Padovani / 66 \\ Problems and Solutions for Markup for Mathematical Examples and Exercises / Georgi Goguadze, Erica Melis, Carsten Ullrich and Paul Cairns / 80 \\ An Annotated Corpus and a Grammar Model of Theorem Description / Yusuke Baba and Masakazu Suzuki / 93 \\ A Query Language for a Metadata Framework about Mathematical Resources / Ferruccio Guidi and Irene Schena / 105 \\ Information Retrieval in MML / Grzegorz Bancerek and Piotr Rudnicki / 119 \\ An Expert System for the Flexible Processing of XML-Based Mathematical Knowledge in a PROLOG-Environment / Bernd D. Heumesser, Dietmar A. Seipel and Ulrich Guntzer / 133 \\ Towards Collaborative Content Management and Version Control for Structured Mathematical Knowledge / Michael Kohlhase and Romeo Anghelache / 147 \\ On the Integrity of a Repository of Formalized Mathematics / Piotr Rudnicki and Andrzej Trybulec / 162 \\ A Theoretical Analysis of Hierarchical Proofs / Paul Cairns and Jeremy Gow / 175 \\ Comparing Mathematical Provers / Freek Wiedijk / 188 \\ Translating Mizar for First Order Theorem Provers / Josef Urban / 203 \\ The Mathematical Semantic Web / Massimo Marchiori / 216 \\ Author Index / 225

entry:
@Proceedings{Asperti:2003:MKM,
  editor =       "Andrea Asperti and Bruno Buchberger and James Harold
                 Davenport",
  booktitle =    "{Mathematical knowledge management: second
                 international conference, MKM 2003, Bertinoro, Italy,
                 February 16--18, 2003: proceedings}",
  title =        "{Mathematical knowledge management: second
                 international conference, MKM 2003, Bertinoro, Italy,
                 February 16--18, 2003: proceedings}",
  volume =       "2594",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 223",
  year =         "2003",
  DOI =          "https://doi.org/10.1007/3540364692",
  ISBN =         "3-540-00568-4 (softcover)",
  ISBN-13 =      "978-3-540-00568-1 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.95 .I565 2003",
  bibdate =      "Sat Aug 13 17:26:10 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in computer science",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0817/2003042408-d.html",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Mathematical Knowledge
                 Management (2nd: 2003: Bertinoro, Italy)",
  subject =      "Mathematics; Data processing; Congresses; Information
                 storage and retrieval systems; Automatic theorem
                 proving",
  tableofcontents = "Digitisation, Representation, and Formalisation
                 (Digital Libraries of Mathematics) / Andrew A. Adams /
                 1 \\
                 MKM from Book to Computer: A Case Study / James H.
                 Davenport / 17 \\
                 From Proof-Assistants to Distributed Libraries of
                 Mathematics: Tips and Pitfalls / Claudio Sacerdoti Coen
                 / 30 \\
                 Managing Digital Mathematical Discourse / Jonathan
                 Borwein and Terry Stanway / 45 \\
                 NAG Library Documentation / David Carlisle and Mike
                 Dewar / 56 \\
                 On the Roles of \LaTeX{} and MathML in Encoding and
                 Processing Mathematical Expressions / Luca Padovani /
                 66 \\
                 Problems and Solutions for Markup for Mathematical
                 Examples and Exercises / Georgi Goguadze, Erica Melis,
                 Carsten Ullrich and Paul Cairns / 80 \\
                 An Annotated Corpus and a Grammar Model of Theorem
                 Description / Yusuke Baba and Masakazu Suzuki / 93 \\
                 A Query Language for a Metadata Framework about
                 Mathematical Resources / Ferruccio Guidi and Irene
                 Schena / 105 \\
                 Information Retrieval in MML / Grzegorz Bancerek and
                 Piotr Rudnicki / 119 \\
                 An Expert System for the Flexible Processing of
                 XML-Based Mathematical Knowledge in a
                 PROLOG-Environment / Bernd D. Heumesser, Dietmar A.
                 Seipel and Ulrich Guntzer / 133 \\
                 Towards Collaborative Content Management and Version
                 Control for Structured Mathematical Knowledge / Michael
                 Kohlhase and Romeo Anghelache / 147 \\
                 On the Integrity of a Repository of Formalized
                 Mathematics / Piotr Rudnicki and Andrzej Trybulec / 162
                 \\
                 A Theoretical Analysis of Hierarchical Proofs / Paul
                 Cairns and Jeremy Gow / 175 \\
                 Comparing Mathematical Provers / Freek Wiedijk / 188
                 \\
                 Translating Mizar for First Order Theorem Provers /
                 Josef Urban / 203 \\
                 The Mathematical Semantic Web / Massimo Marchiori / 216
                 \\
                 Author Index / 225",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Michalos:2003:BTE
editor: Alex C. Michalos
booktitle: The best teacher I ever had: personal reports from highly productive scholars
title: The best teacher I ever had: personal reports from highly productive scholars
publisher: Althouse Press
address: London, ON, Canada
pages: 294
year: 2003
ISBN: 0-920354-53-X OR 092035453X
ISBN13: 978-0-920354-53-7 OR 9780920354537
LCCN: LA2321 .B47 2003
bibdate: Sat Sep 3 08:42:39 MDT 2022
bibtimestamp: 2022.09.03 08:42:39 MDT
acknowledgement: ack-nhfb
rawbooktitle: The best teacher {I} ever had: personal reports from highly productive scholars
raweditor: Alex C. Michalos
rawtitle: The best teacher {I} ever had: personal reports from highly productive scholars
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; fsz3950.oclc.org:210/WorldCat

abstract:
Alex Michalos wondered what Fellows of the Royal Society of Canada would say, if asked to describe their ``best teacher'' and what their answers would disclose about the effect these best teachers had on the lives of some of Canada's most renowned scholars. Names range from C.S. Lewis to J.R.R. Tolkien, from Northrop Frye to Robertson Davies, from A.S.P. Woodhouse to Charles Best to Karl Popper, Bruce Chalmers, and many, many others.

subject:
Teachers; Canada; Anecdotes; Teacher-student relationships; Enseignants; Relations enseignants-eleves; Teacher-student relationships; Teachers

TOC:
1.John (Janos) Aczel on Lipot Fejer and others 2. Joseph Agassi on Karl Popper and other 3. Timothy E. Anna on John Tate Lanning 4. Paul E. Auger on Waldemar Lindgren 5. Karl T. Aust on Bruce Chambers 6. William A. Ayer on Karel Wiesner 7. Morrel P. Bachynski on Leon Katz 8. J. M. Bell on E. W. Crampton 9. R. G. S. Bidwell on Hugh P. Bell and Gleb Krotkov 10. Marie-Claire Blais on Mother Saint-Alfreda 11. Michael Bliss on Evelyn G. Hicks 12. William F. Blissett on Blanche Tilton and others 13. Joseph Bonefant on Robert Ricatte and other 14. Jonathan M. Borwein on David Borwein 15. John M. Bowman on Bruce Chown 16. Albert S. Bregman on William Jarvis McCurdy 17. Mario Bunge on guido Beck 18. Ken Carroll on James McCallum and others 19. Julia Ching on Man Wah Bentley 20. Colin W. Clark on David C. Murdoch 21. Ronald T. Coutts on Mr. McGregor and others 22. Harold G. Coward on Haryy Kreisel 23. James M. Daniels on James Wiles 24. Julian Davies on Mr. Finney and others 25. Henri Dorion on Louis-Edmond Hamelin 26. Leo Dreidger on H. Form and others 27. J. S. Dugdale on G. R. Noakes 28. Peter A. Egelstaff on ``Experience'' 29. Margrit Eichler on Ursula Franklin 30. Keith Ellis on Kurt Leopold Levy 31. J. David Embury on Alan Cottrell and others 32. James Allan Evans on Gordon Keyes 33. Emil L. Fackenheim on Adolph Loercher 34. Thomas Z. Fahidy on Fejes-Toth Laszlo 35. Harold J. Fallding on Jean Craig 36. A. Murray Fallis on F. B. Allan and others 37. Emmanuel Farber on Arthur Worth Ham 38. Tom Flanagan on Gerhart Niemeyer 39. Henry G. Friesen on Joseph Doupe and Edwin Astwood 40. W. S. Fyfe on John Eccles and others 41. George D. Garland on D. A. F. Robinson and others 42. Marc Gaudry on Henri Bouillard and others 43. Eville Gorham on Donald Crowdis and others 44. James Gray on C. S. Lewis 45. Leslie C. Green on L. F. W. White and others 46. Jean Grondin on Hans-George Gadamer 47. Wm. C. Gussow on W. H. Collins and others 48. Jean-Jacques Hamm on Charles Hummel 49. F. Kenneth Hare on Sidney William Woolridge 50. W. E. Harris on Laurine Bergen 51. Constance B. Hieatt on Jessie B. Winterbottom 52. John L. Holmes on J. A. G. Knight 53. Noel Hynes on Monsieur Largier 54. Jack Jacobs on Wlater Gage 55. R. Norman Jones on R. B. Wright 56. Harold Kalant on John Morrow and others 57. Morris Kates on Mr. Doherty 58. W. J. Keith on W. E. Barron and A. P. Rossiter 59. Bryce Kendrick on Will Kendrick 60. Nathan Keyfitz on Mr. Somerville and others 61. Jarmia Kukalova-Peck on Zdenek V. Spinar 62. Walter Kupsch on John Campbell Soroule 63. Phyllis Lambert on Richard Krautheimer 64. Jean Laponce on Andre Siegfried and others 65. Gary P. Latham on H. D. (Ace) Beach 66. Paul H. LeBlond on Ron Burling 67. William C. Leggett on Geoffrey Power 68. John Leslie on Anonymous 69. Kurt Levy on Federico de Onis 70. Douglas G. Lochhead on Robertson Davies and others 71. Kenneth H. Mann on Mr. Coptcoat and others 72. Jean-Claude Marsan on Percy Johnson-Marshall 73. E. A. McCulloch on Almon Fletcher and others 74. Kenneth D. McRae on Harold Innis 75. John Meisel on Pani Sedlakova and others 76. JHugo A. Meynell on Miss Hawkins 77. Andrew D. Miall on Arnold Berry 78. Alex C. Michalos on J. Coert Rylaarsdam 79. William Michelson on Charles Tilly 80. Desmond MOrton on Mme. Sata and others 81. Robert G. E. Murray on Carl F. Robinow 82. M. Ram Murty and V. Kumar Murty on Mothers and others 83. Ralph W. Nicholls on Cyril Baxter 84. Geoff Norris on Mr. Taylor and others 85. Christine Overall on Jack Stevenson 86. Marian A. Packham on John Satterly 87. T. R. Parsons on C. F. Kirby 88. Terence M. Penelhum on Miss Bignell 89. R. Larry Peterson on Harold Brodie 90. Lewis Payton on Russell McCormmach 91. James C. Reaney on Northrop Frye 92. Leonard W. Reeves on Joel Henry Hildebrand 93. D. Regan on Mr. Hinchcliffe and others 94. A. G. Rigg on A. R. Nutt and others 95. Bryon P. Rourke on Joseph Francis Kubis 96. Jean-Louis Roux on Pierre Angers and others 97. Martha Salcudean on Wilhelp Rohonyi 98. Indira V. Samarasekera on Keith Brimacombe 99. William A. Sarjeant on Leslie R. Moore and other 100. Roger M. Savory on Vladimir Fedorovich Minorsky 101. Michael Sayer on George George 102. Benjamin Schlesinger on Ray Godfrey 103. Morris Schnitzer on W. A. DeLong 104. R. J. Schoeck on Jacob Amacher and others 105. Carol Shields on Miss Pelsue 106. David E. Smith on Hartley Thomas and others 107. Victor Snieckus on Rube Sandin 108. Margaret A. Somerville on George Patrick Ganley 109. Francis Sparshott on J. J. C. ``Jack'' Smart 110. George F. G. Stanley on A. L. Burt and others 111. Mary Eileen Stapleton Spencer on H. L. Holmes 112. Peter Suedfeld on Alice Lasker Ginott 113. Clara Thomas on A. S. P. Woodhouse 114. Anne B. Underhill on S. Chandrasekhar 115. M. C. Urquhart on George Alexander Elliott 116. Dennis E. Vance on Benton Naff and others 117. Sidney van den Bergh on Marcel Minnaert 118. Mladen Vranic on Charles Herbert Best 119. P. B. Waite on George Wilson 120. David Waterhouse on Muriel Denny and others 121. Morris Wayman on L. C. M. Pomeroy and Charles G. Fraser 122. Christopher D. Webster on Kasper Neagle and others 123. Roy A. Wise on Donald Olding Hebb 124. John H. Woods on Douglas Poole Dryer

rawabstract:
Alex Michalos wondered what Fellows of the Royal Society of Canada would say, if asked to describe their ``best teacher'' and what their answers would disclose about the effect these best teachers had on the lives of some of Canada's most renowned scholars. Names range from C.S. Lewis to J.R.R. Tolkien, from Northrop Frye to Robertson Davies, from A.S.P. Woodhouse to Charles Best to Karl Popper, Bruce Chalmers, and many, many others.

rawTOC:
1.John (Janos) Aczel on Lipot Fejer and others \\ 2. Joseph Agassi on Karl Popper and other \\ 3. Timothy E. Anna on John Tate Lanning \\ 4. Paul E. Auger on Waldemar Lindgren \\ 5. Karl T. Aust on Bruce Chambers \\ 6. William A. Ayer on Karel Wiesner \\ 7. Morrel P. Bachynski on Leon Katz \\ 8. J. M. Bell on E. W. Crampton \\ 9. R. G. S. Bidwell on Hugh P. Bell and Gleb Krotkov \\ 10. Marie-Claire Blais on Mother Saint-Alfreda \\ 11. Michael Bliss on Evelyn G. Hicks \\ 12. William F. Blissett on Blanche Tilton and others \\ 13. Joseph Bonefant on Robert Ricatte and other \\ 14. Jonathan M. Borwein on David Borwein \\ 15. John M. Bowman on Bruce Chown \\ 16. Albert S. Bregman on William Jarvis McCurdy \\ 17. Mario Bunge on guido Beck \\ 18. Ken Carroll on James McCallum and others \\ 19. Julia Ching on Man Wah Bentley \\ 20. Colin W. Clark on David C. Murdoch \\ 21. Ronald T. Coutts on Mr. McGregor and others \\ 22. Harold G. Coward on Haryy Kreisel \\ 23. James M. Daniels on James Wiles \\ 24. Julian Davies on Mr. Finney and others \\ 25. Henri Dorion on Louis-Edmond Hamelin \\ 26. Leo Dreidger on H. Form and others \\ 27. J. S. Dugdale on G. R. Noakes \\ 28. Peter A. Egelstaff on ``Experience'' \\ 29. Margrit Eichler on Ursula Franklin \\ 30. Keith Ellis on Kurt Leopold Levy \\ 31. J. David Embury on Alan Cottrell and others \\ 32. James Allan Evans on Gordon Keyes \\ 33. Emil L. Fackenheim on Adolph Loercher \\ 34. Thomas Z. Fahidy on Fejes-Toth Laszlo \\ 35. Harold J. Fallding on Jean Craig \\ 36. A. Murray Fallis on F. B. Allan and others \\ 37. Emmanuel Farber on Arthur Worth Ham \\ 38. Tom Flanagan on Gerhart Niemeyer \\ 39. Henry G. Friesen on Joseph Doupe and Edwin Astwood \\ 40. W. S. Fyfe on John Eccles and others \\ 41. George D. Garland on D. A. F. Robinson and others \\ 42. Marc Gaudry on Henri Bouillard and others \\ 43. Eville Gorham on Donald Crowdis and others \\ 44. James Gray on C. S. Lewis \\ 45. Leslie C. Green on L. F. W. White and others \\ 46. Jean Grondin on Hans-George Gadamer \\ 47. Wm. C. Gussow on W. H. Collins and others \\ 48. Jean-Jacques Hamm on Charles Hummel \\ 49. F. Kenneth Hare on Sidney William Woolridge \\ 50. W. E. Harris on Laurine Bergen \\ 51. Constance B. Hieatt on Jessie B. Winterbottom \\ 52. John L. Holmes on J. A. G. Knight \\ 53. Noel Hynes on Monsieur Largier \\ 54. Jack Jacobs on Wlater Gage \\ 55. R. Norman Jones on R. B. Wright \\ 56. Harold Kalant on John Morrow and others \\ 57. Morris Kates on Mr. Doherty \\ 58. W. J. Keith on W. E. Barron and A. P. Rossiter \\ 59. Bryce Kendrick on Will Kendrick \\ 60. Nathan Keyfitz on Mr. Somerville and others \\ 61. Jarmia Kukalova-Peck on Zdenek V. Spinar \\ 62. Walter Kupsch on John Campbell Soroule \\ 63. Phyllis Lambert on Richard Krautheimer \\ 64. Jean Laponce on Andre Siegfried and others \\ 65. Gary P. Latham on H. D. (Ace) Beach \\ 66. Paul H. LeBlond on Ron Burling \\ 67. William C. Leggett on Geoffrey Power \\ 68. John Leslie on Anonymous \\ 69. Kurt Levy on Federico de Onis \\ 70. Douglas G. Lochhead on Robertson Davies and others \\ 71. Kenneth H. Mann on Mr. Coptcoat and others \\ 72. Jean-Claude Marsan on Percy Johnson-Marshall \\ 73. E. A. McCulloch on Almon Fletcher and others \\ 74. Kenneth D. McRae on Harold Innis \\ 75. John Meisel on Pani Sedlakova and others \\ 76. JHugo A. Meynell on Miss Hawkins \\ 77. Andrew D. Miall on Arnold Berry \\ 78. Alex C. Michalos on J. Coert Rylaarsdam \\ 79. William Michelson on Charles Tilly \\ 80. Desmond MOrton on Mme. Sata and others \\ 81. Robert G. E. Murray on Carl F. Robinow \\ 82. M. Ram Murty and V. Kumar Murty on Mothers and others \\ 83. Ralph W. Nicholls on Cyril Baxter \\ 84. Geoff Norris on Mr. Taylor and others \\ 85. Christine Overall on Jack Stevenson \\ 86. Marian A. Packham on John Satterly \\ 87. T. R. Parsons on C. F. Kirby \\ 88. Terence M. Penelhum on Miss Bignell \\ 89. R. Larry Peterson on Harold Brodie \\ 90. Lewis Payton on Russell McCormmach \\ 91. James C. Reaney on Northrop Frye \\ 92. Leonard W. Reeves on Joel Henry Hildebrand \\ 93. D. Regan on Mr. Hinchcliffe and others \\ 94. A. G. Rigg on A. R. Nutt and others \\ 95. Bryon P. Rourke on Joseph Francis Kubis \\ 96. Jean-Louis Roux on Pierre Angers and others \\ 97. Martha Salcudean on Wilhelp Rohonyi \\ 98. Indira V. Samarasekera on Keith Brimacombe \\ 99. William A. Sarjeant on Leslie R. Moore and other \\ 100. Roger M. Savory on Vladimir Fedorovich Minorsky \\ 101. Michael Sayer on George George \\ 102. Benjamin Schlesinger on Ray Godfrey \\ 103. Morris Schnitzer on W. A. DeLong \\ 104. R. J. Schoeck on Jacob Amacher and others \\ 105. Carol Shields on Miss Pelsue \\ 106. David E. Smith on Hartley Thomas and others \\ 107. Victor Snieckus on Rube Sandin \\ 108. Margaret A. Somerville on George Patrick Ganley \\ 109. Francis Sparshott on J. J. C. ``Jack'' Smart \\ 110. George F. G. Stanley on A. L. Burt and others \\ 111. Mary Eileen Stapleton Spencer on H. L. Holmes \\ 112. Peter Suedfeld on Alice Lasker Ginott \\ 113. Clara Thomas on A. S. P. Woodhouse \\ 114. Anne B. Underhill on S. Chandrasekhar \\ 115. M. C. Urquhart on George Alexander Elliott \\ 116. Dennis E. Vance on Benton Naff and others \\ 117. Sidney van den Bergh on Marcel Minnaert \\ 118. Mladen Vranic on Charles Herbert Best \\ 119. P. B. Waite on George Wilson \\ 120. David Waterhouse on Muriel Denny and others \\ 121. Morris Wayman on L. C. M. Pomeroy and Charles G. Fraser \\ 122. Christopher D. Webster on Kasper Neagle and others \\ 123. Roy A. Wise on Donald Olding Hebb \\ 124. John H. Woods on Douglas Poole Dryer

entry:
@Book{Michalos:2003:BTE,
  editor =       "Alex C. Michalos",
  booktitle =    "The best teacher {I} ever had: personal reports from
                 highly productive scholars",
  title =        "The best teacher {I} ever had: personal reports from
                 highly productive scholars",
  publisher =    "Althouse Press",
  address =      "London, ON, Canada",
  pages =        "294",
  year =         "2003",
  ISBN =         "0-920354-53-X",
  ISBN-13 =      "978-0-920354-53-7",
  LCCN =         "LA2321 .B47 2003",
  bibdate =      "Sat Sep 3 08:42:39 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 fsz3950.oclc.org:210/WorldCat",
  abstract =     "Alex Michalos wondered what Fellows of the Royal
                 Society of Canada would say, if asked to describe their
                 ``best teacher'' and what their answers would disclose
                 about the effect these best teachers had on the lives
                 of some of Canada's most renowned scholars. Names range
                 from C.S. Lewis to J.R.R. Tolkien, from Northrop Frye
                 to Robertson Davies, from A.S.P. Woodhouse to Charles
                 Best to Karl Popper, Bruce Chalmers, and many, many
                 others.",
  acknowledgement = ack-nhfb,
  subject =      "Teachers; Canada; Anecdotes; Teacher-student
                 relationships; Enseignants; Relations
                 enseignants-{\'e}l{\`e}ves; Teacher-student
                 relationships; Teachers",
  tableofcontents = "1.John (Janos) Aczel on Lipot Fejer and others \\
                 2. Joseph Agassi on Karl Popper and other \\
                 3. Timothy E. Anna on John Tate Lanning \\
                 4. Paul E. Auger on Waldemar Lindgren \\
                 5. Karl T. Aust on Bruce Chambers \\
                 6. William A. Ayer on Karel Wiesner \\
                 7. Morrel P. Bachynski on Leon Katz \\
                 8. J. M. Bell on E. W. Crampton \\
                 9. R. G. S. Bidwell on Hugh P. Bell and Gleb Krotkov
                 \\
                 10. Marie-Claire Blais on Mother Saint-Alfreda \\
                 11. Michael Bliss on Evelyn G. Hicks \\
                 12. William F. Blissett on Blanche Tilton and others
                 \\
                 13. Joseph Bonefant on Robert Ricatte and other \\
                 14. Jonathan M. Borwein on David Borwein \\
                 15. John M. Bowman on Bruce Chown \\
                 16. Albert S. Bregman on William Jarvis McCurdy \\
                 17. Mario Bunge on guido Beck \\
                 18. Ken Carroll on James McCallum and others \\
                 19. Julia Ching on Man Wah Bentley \\
                 20. Colin W. Clark on David C. Murdoch \\
                 21. Ronald T. Coutts on Mr. McGregor and others \\
                 22. Harold G. Coward on Haryy Kreisel \\
                 23. James M. Daniels on James Wiles \\
                 24. Julian Davies on Mr. Finney and others \\
                 25. Henri Dorion on Louis-Edmond Hamelin \\
                 26. Leo Dreidger on H. Form and others \\
                 27. J. S. Dugdale on G. R. Noakes \\
                 28. Peter A. Egelstaff on ``Experience'' \\
                 29. Margrit Eichler on Ursula Franklin \\
                 30. Keith Ellis on Kurt Leopold Levy \\
                 31. J. David Embury on Alan Cottrell and others \\
                 32. James Allan Evans on Gordon Keyes \\
                 33. Emil L. Fackenheim on Adolph Loercher \\
                 34. Thomas Z. Fahidy on Fejes-Toth Laszlo \\
                 35. Harold J. Fallding on Jean Craig \\
                 36. A. Murray Fallis on F. B. Allan and others \\
                 37. Emmanuel Farber on Arthur Worth Ham \\
                 38. Tom Flanagan on Gerhart Niemeyer \\
                 39. Henry G. Friesen on Joseph Doupe and Edwin Astwood
                 \\
                 40. W. S. Fyfe on John Eccles and others \\
                 41. George D. Garland on D. A. F. Robinson and others
                 \\
                 42. Marc Gaudry on Henri Bouillard and others \\
                 43. Eville Gorham on Donald Crowdis and others \\
                 44. James Gray on C. S. Lewis \\
                 45. Leslie C. Green on L. F. W. White and others \\
                 46. Jean Grondin on Hans-George Gadamer \\
                 47. Wm. C. Gussow on W. H. Collins and others \\
                 48. Jean-Jacques Hamm on Charles Hummel \\
                 49. F. Kenneth Hare on Sidney William Woolridge \\
                 50. W. E. Harris on Laurine Bergen \\
                 51. Constance B. Hieatt on Jessie B. Winterbottom \\
                 52. John L. Holmes on J. A. G. Knight \\
                 53. Noel Hynes on Monsieur Largier \\
                 54. Jack Jacobs on Wlater Gage \\
                 55. R. Norman Jones on R. B. Wright \\
                 56. Harold Kalant on John Morrow and others \\
                 57. Morris Kates on Mr. Doherty \\
                 58. W. J. Keith on W. E. Barron and A. P. Rossiter \\
                 59. Bryce Kendrick on Will Kendrick \\
                 60. Nathan Keyfitz on Mr. Somerville and others \\
                 61. Jarmia Kukalova-Peck on Zdenek V. Spinar \\
                 62. Walter Kupsch on John Campbell Soroule \\
                 63. Phyllis Lambert on Richard Krautheimer \\
                 64. Jean Laponce on Andre Siegfried and others \\
                 65. Gary P. Latham on H. D. (Ace) Beach \\
                 66. Paul H. LeBlond on Ron Burling \\
                 67. William C. Leggett on Geoffrey Power \\
                 68. John Leslie on Anonymous \\
                 69. Kurt Levy on Federico de Onis \\
                 70. Douglas G. Lochhead on Robertson Davies and others
                 \\
                 71. Kenneth H. Mann on Mr. Coptcoat and others \\
                 72. Jean-Claude Marsan on Percy Johnson-Marshall \\
                 73. E. A. McCulloch on Almon Fletcher and others \\
                 74. Kenneth D. McRae on Harold Innis \\
                 75. John Meisel on Pani Sedlakova and others \\
                 76. JHugo A. Meynell on Miss Hawkins \\
                 77. Andrew D. Miall on Arnold Berry \\
                 78. Alex C. Michalos on J. Coert Rylaarsdam \\
                 79. William Michelson on Charles Tilly \\
                 80. Desmond MOrton on Mme. Sata and others \\
                 81. Robert G. E. Murray on Carl F. Robinow \\
                 82. M. Ram Murty and V. Kumar Murty on Mothers and
                 others \\
                 83. Ralph W. Nicholls on Cyril Baxter \\
                 84. Geoff Norris on Mr. Taylor and others \\
                 85. Christine Overall on Jack Stevenson \\
                 86. Marian A. Packham on John Satterly \\
                 87. T. R. Parsons on C. F. Kirby \\
                 88. Terence M. Penelhum on Miss Bignell \\
                 89. R. Larry Peterson on Harold Brodie \\
                 90. Lewis Payton on Russell McCormmach \\
                 91. James C. Reaney on Northrop Frye \\
                 92. Leonard W. Reeves on Joel Henry Hildebrand \\
                 93. D. Regan on Mr. Hinchcliffe and others \\
                 94. A. G. Rigg on A. R. Nutt and others \\
                 95. Bryon P. Rourke on Joseph Francis Kubis \\
                 96. Jean-Louis Roux on Pierre Angers and others \\
                 97. Martha Salcudean on Wilhelp Rohonyi \\
                 98. Indira V. Samarasekera on Keith Brimacombe \\
                 99. William A. Sarjeant on Leslie R. Moore and other
                 \\
                 100. Roger M. Savory on Vladimir Fedorovich Minorsky
                 \\
                 101. Michael Sayer on George George \\
                 102. Benjamin Schlesinger on Ray Godfrey \\
                 103. Morris Schnitzer on W. A. DeLong \\
                 104. R. J. Schoeck on Jacob Amacher and others \\
                 105. Carol Shields on Miss Pelsue \\
                 106. David E. Smith on Hartley Thomas and others \\
                 107. Victor Snieckus on Rube Sandin \\
                 108. Margaret A. Somerville on George Patrick Ganley
                 \\
                 109. Francis Sparshott on J. J. C. ``Jack'' Smart \\
                 110. George F. G. Stanley on A. L. Burt and others \\
                 111. Mary Eileen Stapleton Spencer on H. L. Holmes \\
                 112. Peter Suedfeld on Alice Lasker Ginott \\
                 113. Clara Thomas on A. S. P. Woodhouse \\
                 114. Anne B. Underhill on S. Chandrasekhar \\
                 115. M. C. Urquhart on George Alexander Elliott \\
                 116. Dennis E. Vance on Benton Naff and others \\
                 117. Sidney van den Bergh on Marcel Minnaert \\
                 118. Mladen Vranic on Charles Herbert Best \\
                 119. P. B. Waite on George Wilson \\
                 120. David Waterhouse on Muriel Denny and others \\
                 121. Morris Wayman on L. C. M. Pomeroy and Charles G.
                 Fraser \\
                 122. Christopher D. Webster on Kasper Neagle and others
                 \\
                 123. Roy A. Wise on Donald Olding Hebb \\
                 124. John H. Woods on Douglas Poole Dryer",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Berggren:2004:PSB
editor: Lennart Berggren and Jonathan Borwein and Peter Borwein
booktitle: Pi: a source book
title: Pi: a source book
publisher: pub-SV
address: pub-SV:adr
edition: Third
pages: xx + 797
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6
ISBN: 0-387-20571-3 OR 0387205713
ISBN13: 978-0-387-20571-7 OR 9780387205717
MRclass: 11-00 (01A05 01A75 11-03)
MRnumber: 2065455
MRreviewer: F. Beukers
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
remark: CECM Preprint 2003:210.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawbooktitle: Pi: a source book
raweditor: Lennart Berggren and Jonathan Borwein and Peter Borwein
rawtitle: Pi: a source book
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
Preface to the Third Edition / v Preface to the Second Edition / vi Preface / vii Acknowledgments / x Introduction / xvii 1. The Rhind Mathematical Papyrus --- Problem 50 ($approx $1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 2. Engels / Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 3. Archimedes / Measurement of a Circle --- (-250 B.C.) / The seminal work in which Archimedes presents the first true algorithm for $ pi $ / 7 4. Phillips / Archimedes the Numerical --- Analyst (1981) / A summary of Archimedes' work on the computation of $ pi $ using modem notation / 15 5. Lam and Ang / Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $ pi $ and also examines values for $ pi $ given by Zu Chongzhi (429--500) / 20 6. The Banu Musa: The Measurement of Plane and Solid Figures (--850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 7. Madhava / The Power Series for Arctan and Pi (-1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $ pi $ / 45 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $ pi $ / 51 9. Viete / booktitle Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $ pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 10. Wallis. Computation of $ pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $ pi $ that bears his name / 68 11. Wallis / booktitle Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $ 4 / pi $ / ?? 12. Huygens / booktitle De Circuli Magnitudine Inventa (1654) / Huygens's demonstration of how to triple the number of correct decimals over those in Archimedes' estimate of $ pi $ / 81 13. Gregory / Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power / 87 14. Roy / The Discovery of the Series Formula for $ pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $ pi / 4 = 1 - 1/3 + 1/5 - cdots $ / 92 15. Jones / The First Use of $ pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the booktitle Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 16. Newton / Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $ pi $ to 16 decimal places / 110 17. Euler / Chapter 10 of booktitle Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $ pi $ and powers of $ pi $ / 112 18. Lambert / booktitle Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $ pi $ / 129 19. Lambert / Irrationality of $ pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $ pi $ / 141 20. Shanks / Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shanks's report of his monumental hand calculation of $ pi $ / 147 21. Hermite / booktitle Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $ e $ / 162 22. Lindemann / booktitle Ueber die Zahl $ pi $ (1882) / The first proof of the transcendence of $ pi $ / 194 23. Weierstrass / booktitle Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $ pi $ / 207 24. Hilbert / booktitle Ueber die Transzendenz der Zahlen $ e $ und $ pi $ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $ e $ and $ pi $ / 226 25. Goodwin / Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $ pi $ in Indiana / 230 26. Edington / House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $ pi $ (including a copy of the actual bill that was proposed) / 231 27. Singmaster / The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $ pi $ / 236 28. Ramanujan / Squaring the Circle (1913) / A geometric approximation to $ pi $ / 240 29. Ramanujan / Modular Equations and Approximations to $ pi $ (1914) / Ramanujan's seminal paper on pi that includes a number of striking series and algebraic approximations / 241 30. Watson / The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / ?? 31. Ballantine / The Best (?) Formula for Computing $ pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $ pi $ more cleverly / 271 32. Birch / An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $ pi / 4$ as a sum of arctan relations in powers of 10 / 274 33. Niven / A Simple Proof that $ pi $ is Irrational (1947) / A very concise proof of the irrationality of $ pi $ / 276 34. Reitwiesner / An ENIAC Determination of $ pi $ and $ e $ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 35. Schepler / The Chronology of Pi (1950) / A fairly reliable outline of the history of $ pi $ from 3000 B.C. to 1949 / 282 36. Mahler / On the Approximation of $ pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $ pi $ from a given rational or algebraic number.'' / 306 37. Wrench, Jr. / The Evolution of Extended Decimal Approximations to $ pi $ (1960) / A history of the calculation of the digits of $ pi $ to 1960 / 319 38. Shanks and Wrench, Jr. / Calculation of $ pi $ to 100,000 Decimals (1962) / A landmark computation of $ pi $ to more than 100,000 places / 326 39. Sweeny / On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker / Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 41. Adams / Asymptotic Diophantine Approximations to e (1966) / An asymptotic estimate for the rational approximation to $ e $ which disproves the conjecture that $ e $ behaves like almost all numbers in this respect / 368 42. Mahler / Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves / In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $ pi $ / 456 44. Eves / Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $ pi $ / 402 45. Todd / The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 46. Salamin / Computation of $ pi $ Using Arithmetic--Geometric Mean (1976) / The first quadratically converging algorithm for $ pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 47. Brent / Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss--Legendre' method and some different algorithms for $log $ and $exp $ (using Landen transformations).'' / 424 48. Beukers / A Note on the Irrationality of $ zeta (2) $ and $ zeta (3) $ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $zeta (3)$ (and $zeta (2)$) / 434 49. van der Poorten / A Proof that Euler Missed ldots Apery's Proof of the Irrationality of $zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $zeta (3)$ / 439 50. Brent and McMillan / Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high-precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 51. Apostol / A Proof that Euler Missed: Evaluating $zeta (2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $zeta (2) = pi ^2 / 6$ / 456 52. O'Shaughnessy / Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 53. Stern / A Remarkable Approximation to $ pi $ (1985) / Justification of the value of $ pi $ in the Bible through numerological interpretations / 460 54. Newman and Shanks / On a Sequence Arising in Series for $ pi $ (1984) / More connections between $ pi $ and modular equations / 462 55. Cox / The Arithmetic--Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 56. Borwein and Borwein / The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $ pi $) / 537 57. Newman / A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $ e^x $ and $ pi $ using the Gauss AGM without explicit elliptic function theory / 553 58. Wagon / Is Pi Normal? (1985) / A discussion of the conjecture that $ pi $ has randomly distributed digits / 557 59. Keith / Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $ pi $ / 560 60. Bailey / The Computation of $ pi $ to 29,360,000 Decimal Digits Using Borwein's Quartically Convergent Algorithm (1988) / The algorithms used, both for $ pi $ and for performing the required multiple-precision arithmetic / 562 61. Kanada / Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of $ pi $ Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $ pi $ / 576 62. Borwein and Borwein / Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $ pi $, and how his approach is now incorporated into modern computer algorithms / 588 63. Chudnovsky and Chudnovsky / Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $ pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 64. Borwein, Borwein and Bailey / Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $ pi $ using mathematics rooted in Ramanujan's work / 623 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $ pi $, truncated at 500,000 terms, gives $ pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 66. Beukers, Bezivin, and Robba / An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 67. Webster / The Tale of Pi (1991) / Various anecdotes about $ pi $ from the 14th annual IMO Lecture to the Royal Society / 654 68. Eco / An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 69. Keith / Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $ pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 70. Bailey, Borwein, and Plouffe / On the Rapid Computation of Various Polylogarithmic Constants (1997) / A fast method for computing individual digits of $ pi $ in base 2 / 663 Appendix I --- On the Early History of Pi / 677 Appendix II --- A Computational Chronology of Pi / 683 Appendix III --- Selected Formulae for Pi / 686 Appendix IV --- Translations of Viele and Huygens / 690 Bibliography / 710 Credits / 717 A Pamphlet on Pi / 721 Contents / 723 1. Pi and Its Friends / 725 2. Normality of Numbers / 741 3. Historia Cyclometrica / 753 4. Demotica Cyclometrica / 771 References / 779 Index / 783

rawTOC:
Preface to the Third Edition / v \\ Preface to the Second Edition / vi \\ Preface / vii \\ Acknowledgments / x \\ Introduction / xvii \\ 1. The Rhind Mathematical Papyrus --- Problem 50 ($\approx$1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ 2. Engels / Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ 3. Archimedes / Measurement of a Circle --- (-250 B.C.) / The seminal work in which Archimedes presents the first true algorithm for $ \pi $ / 7 \\ 4. Phillips / Archimedes the Numerical --- Analyst (1981) / A summary of Archimedes' work on the computation of $ \pi $ using modem notation / 15 \\ 5. Lam and Ang / Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $ \pi $ and also examines values for $ \pi $ given by Zu Chongzhi (429--500) / 20 \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures (--850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ 7. M{\=a}dhava / The Power Series for Arctan and Pi (-1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $ \pi $ / 45 \\ 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $ \pi $ / 51 \\ 9. Vi{\`e}te / \booktitle{Variorum de Rebus Mathematicis Reponsorum Liber VII} (1593) / Two excerpts. One containing the first infinite expression of $ \pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ 10. Wallis. Computation of $ \pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $ \pi $ that bears his name / 68 \\ 11. Wallis / \booktitle{Arithmetica Infinitorum} (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $ 4 / \pi$ / ?? \\ 12. Huygens / \booktitle{De Circuli Magnitudine Inventa} (1654) / Huygens's demonstration of how to triple the number of correct decimals over those in Archimedes' estimate of $ \pi $ / 81 13. Gregory / Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power / 87 \\ 14. Roy / The Discovery of the Series Formula for $ \pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $ \pi / 4 = 1 - 1/3 + 1/5 - \cdots{} $ / 92 \\ 15. Jones / The First Use of $ \pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the \booktitle{Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics}, London, 1706 / 108 \\ 16. Newton / Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $ \pi $ to 16 decimal places / 110 \\ 17. Euler / Chapter 10 of \booktitle{Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series)} (1748) / This includes many of Euler's infinite series for $ \pi $ and powers of $ \pi $ / 112 \\ 18. Lambert / \booktitle{M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques} (1761) / An excerpt from Lambert's original proof of the irrationality of $ \pi $ / 129 19. Lambert / Irrationality of $ \pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $ \pi $ / 141 \\ 20. Shanks / Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shanks's report of his monumental hand calculation of $ \pi $ / 147 \\ 21. Hermite / \booktitle{Sur La Fonction Exponentielle} (1873) / The first proof of the transcendence of $ e $ / 162 \\ 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $} (1882) / The first proof of the transcendence of $ \pi $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) / Weierstrass' proof of the transcendence of $ \pi $ / 207 24. Hilbert / \booktitle{Ueber die Transzendenz der Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $ \pi $ in Indiana / 230 \\ 26. Edington / House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $ \pi $ (including a copy of the actual bill that was proposed) / 231 \\ 27. Singmaster / The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $ \pi $ / 236 \\ 28. Ramanujan / Squaring the Circle (1913) / A geometric approximation to $ \pi $ / 240 \\ 29. Ramanujan / Modular Equations and Approximations to $ \pi $ (1914) / Ramanujan's seminal paper on pi that includes a number of striking series and algebraic approximations / 241 \\ 30. Watson / The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / ?? \\ 31. Ballantine / The Best (?) Formula for Computing $ \pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $ \pi $ more cleverly / 271 \\ 32. Birch / An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $ \pi / 4$ as a sum of arctan relations in powers of 10 / 274 \\ 33. Niven / A Simple Proof that $ \pi $ is Irrational (1947) / A very concise proof of the irrationality of $ \pi $ / 276 \\ 34. Reitwiesner / An ENIAC Determination of $ \pi $ and $ e $ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ 35. Schepler / The Chronology of Pi (1950) / A fairly reliable outline of the history of $ \pi $ from 3000 B.C. to 1949 / 282 \\ 36. Mahler / On the Approximation of $ \pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $ \pi $ from a given rational or algebraic number.'' / 306 \\ 37. Wrench, Jr. / The Evolution of Extended Decimal Approximations to $ \pi $ (1960) / A history of the calculation of the digits of $ \pi $ to 1960 / 319 \\ 38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to 100,000 Decimals (1962) / A landmark computation of $ \pi $ to more than 100,000 places / 326 39. Sweeny / On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker / Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ 41. Adams / Asymptotic Diophantine Approximations to e (1966) / An asymptotic estimate for the rational approximation to $ e $ which disproves the conjecture that $ e $ behaves like almost all numbers in this respect / 368 \\ 42. Mahler / Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves / In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $ \pi $ / 456 \\ 44. Eves / Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $ \pi $ / 402 45. Todd / The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ 46. Salamin / Computation of $ \pi $ Using Arithmetic--Geometric Mean (1976) / The first quadratically converging algorithm for $ \pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ 47. Brent / Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss--Legendre' method and some different algorithms for $\log$ and $\exp$ (using Landen transformations).'' / 424 \\ 48. Beukers / A Note on the Irrationality of $ \zeta(2) $ and $ \zeta(3) $ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ 49. van der Poorten / A Proof that Euler Missed \ldots{} Apery's Proof of the Irrationality of $\zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $\zeta (3)$ / 439 \\ 50. Brent and McMillan / Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high-precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ 51. Apostol / A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi^2 / 6$ / 456 \\ 52. O'Shaughnessy / Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ 53. Stern / A Remarkable Approximation to $ \pi $ (1985) / Justification of the value of $ \pi $ in the Bible through numerological interpretations / 460 \\ 54. Newman and Shanks / On a Sequence Arising in Series for $ \pi $ (1984) / More connections between $ \pi $ and modular equations / 462 \\ 55. Cox / The Arithmetic--Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ 56. Borwein and Borwein / The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $ \pi $) / 537 57. Newman / A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $ e^x $ and $ \pi $ using the Gauss AGM without explicit elliptic function theory / 553 \\ 58. Wagon / Is Pi Normal? (1985) / A discussion of the conjecture that $ \pi $ has randomly distributed digits / 557 \\ 59. Keith / Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $ \pi $ / 560 \\ 60. Bailey / The Computation of $ \pi $ to 29,360,000 Decimal Digits Using Borwein's Quartically Convergent Algorithm (1988) / The algorithms used, both for $ \pi $ and for performing the required multiple-precision arithmetic / 562 \\ 61. Kanada / Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of $ \pi $ Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $ \pi $ / 576 \\ 62. Borwein and Borwein / Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $ \pi $, and how his approach is now incorporated into modern computer algorithms / 588 \\ 63. Chudnovsky and Chudnovsky / Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $ \pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ 64. Borwein, Borwein and Bailey / Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $ \pi $ using mathematics rooted in Ramanujan's work / 623 \\ 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $ \pi $, truncated at 500,000 terms, gives $ \pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ 66. Beukers, Bezivin, and Robba / An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ 67. Webster / The Tale of Pi (1991) / Various anecdotes about $ \pi $ from the 14th annual IMO Lecture to the Royal Society / 654 \\ 68. Eco / An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ 69. Keith / Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $ \pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ 70. Bailey, Borwein, and Plouffe / On the Rapid Computation of Various Polylogarithmic Constants (1997) / A fast method for computing individual digits of $ \pi $ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ Appendix II --- A Computational Chronology of Pi / 683 \\ Appendix III --- Selected Formulae for Pi / 686 \\ Appendix IV --- Translations of Viele and Huygens / 690 \\ Bibliography / 710 \\ Credits / 717 \\ A Pamphlet on Pi / 721 \\ Contents / 723 \\ 1. Pi and Its Friends / 725 \\ 2. Normality of Numbers / 741 \\ 3. Historia Cyclometrica / 753 \\ 4. Demotica Cyclometrica / 771 \\ References / 779 \\ Index / 783

entry:
@Book{Berggren:2004:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xx + 797",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6",
  ISBN =         "0-387-20571-3",
  ISBN-13 =      "978-0-387-20571-7",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "2065455",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:210.",
  tableofcontents = "Preface to the Third Edition / v \\
                 Preface to the Second Edition / vi \\
                 Preface / vii \\
                 Acknowledgments / x \\
                 Introduction / xvii \\
                 1. The Rhind Mathematical Papyrus --- Problem 50
                 ($\approx$1650 B.C.) / A problem dealing with the area
                 of a round field of given diameter / 1 \\
                 2. Engels / Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 3. Archimedes / Measurement of a Circle --- (-250 B.C.)
                 / The seminal work in which Archimedes presents the
                 first true algorithm for $ \pi $ / 7 \\
                 4. Phillips / Archimedes the Numerical --- Analyst
                 (1981) / A summary of Archimedes' work on the
                 computation of $ \pi $ using modem notation / 15 \\
                 5. Lam and Ang / Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $ \pi $ and also examines values for $ \pi $
                 given by Zu Chongzhi (429--500) / 20 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures (--850) / This extract gives an
                 explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 7. M{\=a}dhava / The Power Series for Arctan and Pi
                 (-1400) / These theorems by a fifteenth century Indian
                 mathematician give Gregory's series for arctan with
                 remainder terms and Leibniz's series for $ \pi $ / 45
                 \\
                 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $ \pi $ / 51 \\
                 9. Vi{\`e}te / \booktitle{Variorum de Rebus
                 Mathematicis Reponsorum Liber VII} (1593) / Two
                 excerpts. One containing the first infinite expression
                 of $ \pi $, obtained by relating the area of a regular
                 $2n$-gon to that of a regular $n$-gon / 53 \\
                 10. Wallis. Computation of $ \pi $ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $ \pi $ that bears his name / 68 \\
                 11. Wallis / \booktitle{Arithmetica Infinitorum} (1655)
                 / An excerpt including Prop. 189, 191 and an alternate
                 form of the result that gives Wm. Brounker's continued
                 fraction expression for $ 4 / \pi$ / ?? \\
                 12. Huygens / \booktitle{De Circuli Magnitudine
                 Inventa} (1654) / Huygens's demonstration of how to
                 triple the number of correct decimals over those in
                 Archimedes' estimate of $ \pi $ / 81 13. Gregory /
                 Correspondence with John Collins (1671) / A letter to
                 Collins in which he gives his series for arctangent,
                 carried to the ninth power / 87 \\
                 14. Roy / The Discovery of the Series Formula for $ \pi
                 $ by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $ \pi / 4 = 1
                 - 1/3 + 1/5 - \cdots{} $ / 92 \\
                 15. Jones / The First Use of $ \pi $ for the Circle
                 Ratio (1706) / An excerpt from Jones' book, the
                 \booktitle{Synopsis Palmariorum Matheseos: or, a New
                 Introduction to the Mathematics}, London, 1706 / 108
                 \\
                 16. Newton / Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $ \pi $ to 16 decimal places / 110 \\
                 17. Euler / Chapter 10 of \booktitle{Introduction to
                 Analysis of the Infinite (On the Use of the Discovered
                 Fractions to Sum Infinite Series)} (1748) / This
                 includes many of Euler's infinite series for $ \pi $
                 and powers of $ \pi $ / 112 \\
                 18. Lambert / \booktitle{M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques} (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $ \pi $ / 129 19. Lambert /
                 Irrationality of $ \pi $ (1969) / A translation and
                 Struik's discussion of Lambert's proof of the
                 irrationality of $ \pi $ / 141 \\
                 20. Shanks / Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shanks's report
                 of his monumental hand calculation of $ \pi $ / 147 \\
                 21. Hermite / \booktitle{Sur La Fonction Exponentielle}
                 (1873) / The first proof of the transcendence of $ e $
                 / 162 \\
                 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
                 (1882) / The first proof of the transcendence of $ \pi
                 $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
                 Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
                 Weierstrass' proof of the transcendence of $ \pi $ /
                 207 24. Hilbert / \booktitle{Ueber die Transzendenz der
                 Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and
                 elegant simplification of the transcendence proofs for
                 $ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the
                 Circle (1894) / The dubious origin of the attempted
                 legislation of the value of $ \pi $ in Indiana / 230
                 \\
                 26. Edington / House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $ \pi $ (including a copy of the actual bill that
                 was proposed) / 231 \\
                 27. Singmaster / The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $ \pi $ / 236 \\
                 28. Ramanujan / Squaring the Circle (1913) / A
                 geometric approximation to $ \pi $ / 240 \\
                 29. Ramanujan / Modular Equations and Approximations to
                 $ \pi $ (1914) / Ramanujan's seminal paper on pi that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 30. Watson / The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / ?? \\
                 31. Ballantine / The Best (?) Formula for Computing $
                 \pi $ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $ \pi $ more cleverly /
                 271 \\
                 32. Birch / An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $ \pi / 4$ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 33. Niven / A Simple Proof that $ \pi $ is Irrational
                 (1947) / A very concise proof of the irrationality of $
                 \pi $ / 276 \\
                 34. Reitwiesner / An ENIAC Determination of $ \pi $ and
                 $ e $ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 35. Schepler / The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $ \pi $ from 3000
                 B.C. to 1949 / 282 \\
                 36. Mahler / On the Approximation of $ \pi $ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $ \pi $ from a given rational or algebraic number.''
                 / 306 \\
                 37. Wrench, Jr. / The Evolution of Extended Decimal
                 Approximations to $ \pi $ (1960) / A history of the
                 calculation of the digits of $ \pi $ to 1960 / 319 \\
                 38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to
                 100,000 Decimals (1962) / A landmark computation of $
                 \pi $ to more than 100,000 places / 326 39. Sweeny / On
                 the Computation of Euler's Constant (1963) / The
                 computation of Euler's constant to 3566 decimal places
                 / 350 40. Baker / Approximations to the Logarithms of
                 Certain Rational Numbers (1964) / The main purpose of
                 this deep and fundamental paper is to ``deduce results
                 concerning the accuracy with which the natural
                 logarithms of certain rational numbers may be
                 approximated by rational numbers, or, more generally,
                 by algebraic numbers of bounded degree.'' / 359 \\
                 41. Adams / Asymptotic Diophantine Approximations to e
                 (1966) / An asymptotic estimate for the rational
                 approximation to $ e $ which disproves the conjecture
                 that $ e $ behaves like almost all numbers in this
                 respect / 368 \\
                 42. Mahler / Applications of Some Formulae by Hermite
                 to the Approximations of Exponentials of Logarithms
                 (1967) / An important extension of Hilbert's approach
                 to the study of transcendence / 372 43. Eves / In
                 Mathematical Circles; A Selection of Mathematical
                 Stories and Anecdotes (excerpt) (1969) / A collection
                 of mathematical stories and anecdotes about $ \pi $ /
                 456 \\
                 44. Eves / Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $ \pi $ / 402 45. Todd /
                 The Lemniscate Constants (1975) / A unifying account of
                 some of the methods used for computing the lemniscate
                 constants / 412 \\
                 46. Salamin / Computation of $ \pi $ Using
                 Arithmetic--Geometric Mean (1976) / The first
                 quadratically converging algorithm for $ \pi $ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 47. Brent / Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss--Legendre' method and some different algorithms
                 for $\log$ and $\exp$ (using Landen transformations).''
                 / 424 \\
                 48. Beukers / A Note on the Irrationality of $ \zeta(2)
                 $ and $ \zeta(3) $ (1979) / A short and elegant
                 recasting of Apery's proof of the irrationality of
                 $\zeta(3)$ (and $\zeta(2)$) / 434 \\
                 49. van der Poorten / A Proof that Euler Missed
                 \ldots{} Apery's Proof of the Irrationality of $\zeta
                 (3)$ (1979) / An illuminating account of Apery's
                 astonishing proof of the irrationality of $\zeta (3)$ /
                 439 \\
                 50. Brent and McMillan / Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high-precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 51. Apostol / A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi^2 / 6$ / 456 \\
                 52. O'Shaughnessy / Putting God Back in Math (1983) /
                 An article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 53. Stern / A Remarkable Approximation to $ \pi $
                 (1985) / Justification of the value of $ \pi $ in the
                 Bible through numerological interpretations / 460 \\
                 54. Newman and Shanks / On a Sequence Arising in Series
                 for $ \pi $ (1984) / More connections between $ \pi $
                 and modular equations / 462 \\
                 55. Cox / The Arithmetic--Geometric Mean of Gauss
                 (1984) / An extensive study of the complex analytic
                 properties of the AGM / 481 \\
                 56. Borwein and Borwein / The Arithmetic--Geometric
                 Mean and Fast Computation of Elementary Functions
                 (1984) / The relationship between the AGM iteration and
                 fast computation of elementary functions (one of the
                 by-products is an algorithm for $ \pi $) / 537 57.
                 Newman / A Simplified Version of the Fast Algorithms of
                 Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $ e^x $ and $ \pi $ using the Gauss AGM
                 without explicit elliptic function theory / 553 \\
                 58. Wagon / Is Pi Normal? (1985) / A discussion of the
                 conjecture that $ \pi $ has randomly distributed digits
                 / 557 \\
                 59. Keith / Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $ \pi $ / 560 \\
                 60. Bailey / The Computation of $ \pi $ to 29,360,000
                 Decimal Digits Using Borwein's Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $ \pi
                 $ and for performing the required multiple-precision
                 arithmetic / 562 \\
                 61. Kanada / Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of $
                 \pi $ Calculation (1988) / Details of the computation
                 and statistical tests of the first 200 million digits
                 of $ \pi $ / 576 \\
                 62. Borwein and Borwein / Ramanujan and Pi (1988) /
                 This article documents Ramanujan's life, his ingenious
                 approach to calculating $ \pi $, and how his approach
                 is now incorporated into modern computer algorithms /
                 588 \\
                 63. Chudnovsky and Chudnovsky / Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $ \pi $ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 64. Borwein, Borwein and Bailey / Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $ \pi $ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $ \pi $,
                 truncated at 500,000 terms, gives $ \pi $ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 66. Beukers, Bezivin, and Robba / An Alternative Proof
                 of the Lindemann--Weierstrass Theorem (1990) / The
                 Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 67. Webster / The Tale of Pi (1991) / Various anecdotes
                 about $ \pi $ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 68. Eco / An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 69. Keith / Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $ \pi $ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 70. Bailey, Borwein, and Plouffe / On the Rapid
                 Computation of Various Polylogarithmic Constants (1997)
                 / A fast method for computing individual digits of $
                 \pi $ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 Appendix IV --- Translations of Viele and Huygens / 690
                 \\
                 Bibliography / 710 \\
                 Credits / 717 \\
                 A Pamphlet on Pi / 721 \\
                 Contents / 723 \\
                 1. Pi and Its Friends / 725 \\
                 2. Normality of Numbers / 741 \\
                 3. Historia Cyclometrica / 753 \\
                 4. Demotica Cyclometrica / 771 \\
                 References / 779 \\
                 Index / 783",
}


