2000

Pi: A Source Book

Authors:

ISBN: 978-1-4757-3242-9 (Print) 978-1-4757-3240-5 (Online)

Table of contents (70 chapters)

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  1. Front Matter

    Pages i-xix

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    Book Chapter

    Pages 1-2

    The Rhind Mathematical Papyrus-Problem 50 ( ~ 1650 B.C.)

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    Book Chapter

    Pages 3-6

    Quadrature of the Circle in Ancient Egypt

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    Pages 7-14

    Measurement of a Circle

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    Pages 15-19

    Archimedes the Numerical Analyst

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    Pages 20-35

    Circle Measurements in Ancient China

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    Pages 36-44

    The Banū Mūsā: The Measurement of Plane and Solid Figures ( ~ 850)

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    Pages 45-50

    Mādhava. The Power Series for Arctan and Pi ( ~ 1400)

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    Book Chapter

    Pages 51-52

    Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938)

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    Pages 53-67

    Viète. Variorum de Rebus Mathematicis Reponsorum Liber VIII (1593)

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    Book Chapter

    Pages 68-77

    Wallis. Computation of π by Successive Interpolations (1655)

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    Book Chapter

    Pages 78-80

    Wallis. Arithmetica Infinitorum (1655)

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    Book Chapter

    Pages 81-87

    Huygens. De Circuli Magnitudine Inventa (1724)

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    Book Chapter

    Pages 87-91

    Gregory. Correspondence with John Collins (1671)

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    Pages 92-107

    The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha

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    Book Chapter

    Pages 108-109

    The First Use of π for the Circle Ratio (1706)

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    Book Chapter

    Pages 110-111

    Newton.Of the Method of Fluxions and Infinite Series (1737)

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    Pages 112-128

    On the Use of the Discovered Factors to Sum Infinite Series

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    Book Chapter

    Pages 129-140

    Mémoire Sur Quelques Propriétiés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques

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    Book Chapter

    Pages 141-146

    Lambert. Irrationality of π

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    Book Chapter

    Pages 147-161

    Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals

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