Book 1997

Pi: A Source Book

Authors:

ISBN: 978-1-4757-2738-8 (Print) 978-1-4757-2736-4 (Online)

Table of contents (70 chapters)

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  1. Front Matter

    Pages i-xix

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    Chapter

    Pages 1-2

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

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    Chapter

    Pages 3-6

    Quadrature of the Circle in Ancient Egypt

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    Chapter

    Pages 7-14

    Measurement of a Circle

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    Chapter

    Pages 15-19

    Archimedes the Numerical Analyst

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    Chapter

    Pages 20-35

    Circle Measurements in Ancient China

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    Chapter

    Pages 36-44

    The Measurement of Plane and Solid Figures (~850)

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    Chapter

    Pages 45-50

    The Power Series of Arctan and Pi (~1400)

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    Chapter

    Pages 51-52

    Ludolph (or Ludolff or Lucius) van Ceulen

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    Chapter

    Pages 53-67

    Variorum de Rebus Mathematicis Reponsorum Liber VII (1593)

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    Chapter

    Pages 68-77

    Computation of π by Successive Interpolations

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    Chapter

    Pages 78-80

    Arithmetica Infinitorum (1655)

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    Chapter

    Pages 81-86

    De Circuli Magnitudine Inventa

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    Chapter

    Pages 87-91

    Correspondence with John Collins (1671)

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    Chapter

    Pages 92-107

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

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    Chapter

    Pages 108-109

    The First Use of π for the Circle Ratio

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    Chapter

    Pages 110-111

    Of the Method of Fluxions and Infinite Series (1737)

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    Chapter

    Pages 112-128

    On the Use of the Discovered Factors to Sum Infinite Series

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    Chapter

    Pages 129-140

    Mémoire Sur Quelques Propriétés Remarquables des Quantités Transcendentes Circulaires et Logarithmiques

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    Chapter

    Pages 141-146

    Lambert. Irrationality of π

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    Chapter

    Pages 147-161

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

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