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Pi: A Source Book

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Cover of 'Pi: A Source Book'

Table of Contents

  1. Altmetric Badge
    Book Overview
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    Chapter 1 The Rhind Mathematical Papyrus-Problem 50 ( ~ 1650 B.C.)
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    Chapter 2 Quadrature of the Circle in Ancient Egypt
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    Chapter 3 Measurement of a Circle
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    Chapter 4 Archimedes the Numerical Analyst
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    Chapter 5 Circle Measurements in Ancient China
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    Chapter 6 The Banū Mūsā: The Measurement of Plane and Solid Figures ( ~ 850)
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    Chapter 7 Mādhava. The Power Series for Arctan and Pi ( ~ 1400)
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    Chapter 8 Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938)
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    Chapter 9 Viète. Variorum de Rebus Mathematicis Reponsorum Liber VIII (1593)
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    Chapter 10 Wallis. Computation of π by Successive Interpolations (1655)
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    Chapter 11 Wallis. Arithmetica Infinitorum (1655)
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    Chapter 12 Huygens. De Circuli Magnitudine Inventa (1724)
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    Chapter 13 Gregory. Correspondence with John Collins (1671)
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    Chapter 14 The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha
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    Chapter 15 The First Use of π for the Circle Ratio (1706)
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    Chapter 16 Newton.Of the Method of Fluxions and Infinite Series (1737)
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    Chapter 17 On the Use of the Discovered Factors to Sum Infinite Series
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    Chapter 18 Mémoire Sur Quelques Propriétiés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques
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    Chapter 19 Lambert. Irrationality of π
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    Chapter 20 Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals
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    Chapter 21 Sur la Fonction Exponentielle
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    Chapter 22 Ueber die Zahl π
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    Chapter 23 Zu Lindemann’s , Abhandlung: „Über die Ludolph ’sche Zahl“
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    Chapter 24 Ueber die Transcendenz der Zahlen e und π
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    Chapter 25 Quadrature of the Circle
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    Chapter 26 House Bill No. 246, Indiana State Legislature, 1897
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    Chapter 27 The Legal Values of Pi
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    Chapter 28 Squaring the Circle
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    Chapter 29 Modular Equations and Approximations to π
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    Chapter 30 The Marquis and the Land-Agent; A Tale of the Eighteenth Century
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    Chapter 31 The Best (?) Formula for Computing π to a Thousand Places
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    Chapter 32 An Algorithm for the Construction of Arctangent Relations
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    Chapter 33 A Simple Proof that π is Irrational
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    Chapter 34 An ENIAC Determination of π and e to more than 2000 Decimal Places
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    Chapter 35 The Chronology of Pi
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    Chapter 36 On the Approximation of π
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    Chapter 37 The evolution of extended decimal approximations to π
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    Chapter 38 Calculation of π to 100,000 Decimals
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    Chapter 39 On the Computation of Euler’s Constant
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    Chapter 40 Approximations to the logarithms of certain rational numbers
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    Chapter 41 Asymptotic Diophantine Approximations to E
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    Chapter 42 Applications of Some Formulae by Hermite to the Approximation of Exponentials and Logarithms
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    Chapter 43 Mathematical Circles: A Selection of Mathematical Stories and Anecdotes
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    Chapter 44 Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt)
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    Chapter 45 The Lemniscate Constants
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    Chapter 46 Computation of π Using Arithmetic-Geometric Mean
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    Chapter 47 Fast Multiple-Precision Evaluation of Elementary Functions
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    Chapter 48 A Note on the Irrationality of ζ (2) and ζ (3)
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    Chapter 49 A Proof that Euler Missed …
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    Chapter 50 Some New Algorithms for High-Precision Computation of Euler’s Constant
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    Chapter 51 A Proof that Euler Missed: Evaluating ξ(2) the Easy Way
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    Chapter 52 Putting God Back In Math
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    Chapter 53 69.30 A remarkable approximation to π
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    Chapter 54 On a Sequence Arising in Series for π
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    Chapter 55 The Arithmetic-Geometric Mean of Gauss
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    Chapter 56 The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
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    Chapter 57 A Simplified Version of the Fast Algorithms of Brent and Salamin
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    Chapter 58 Is π Normal?
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    Chapter 59 Circle Digits A Self-Referential Story
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    Chapter 60 The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm
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    Chapter 61 Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of π Calculation
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    Chapter 62 Ramanujan and Pi
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    Chapter 63 Approximations and complex multiplication according to Ramanujan
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    Chapter 64 Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
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    Chapter 65 Pi, Euler Numbers, and Asymptotic Expansions
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    Chapter 66 An Alternative Proof of the Lindemann-Weierstrass Theorem
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    Chapter 67 The Tail of π
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    Chapter 68 Eco. An excerpt from Foucault’s Pendulum (1993)
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    Chapter 69 Pi Mnemonics and the Art of Constrained Writing
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    Chapter 70 On the Rapid Computation of Various Polylogarithmic Constants
Overall attention for this book and its chapters
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1 Google+ user

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mendeley
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Title
Pi: A Source Book
Published by
Springer New York, January 2000
DOI 10.1007/978-1-4757-3240-5
ISBNs
978-1-4757-3242-9, 978-1-4757-3240-5
Authors

Berggren, Lennart, Borwein, Jonathan, Borwein, Peter

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 2 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 2 100%

Demographic breakdown

Readers by professional status Count As %
Researcher 1 50%
Unknown 1 50%
Readers by discipline Count As %
Computer Science 1 50%
Unknown 1 50%