Pi: A Source Book

Authors: Borwein, Jonathan M.

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About this book

Our intention in this collection is to provide, largely through original writings, an ex­ tended account 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 most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi­ cant number of the most important mathematicians have contributed to its unfolding­ directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog­ nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe­ maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected.

Reviews

From the reviews:

"Few mathematics books serve a wider potential readership than does a source book and this particular one is admirably designed to cater for a broad spectrum of tastes: professional mathematicians with research interest in related subjects, historians of mathematics, teachers at all levels searching out material for individual talks and student projects, and amateurs who will find much to amuse and inform them in this leafy tome. The authors are to be congratulated on their good taste in preparing such a rich and varied banquet with which to celebrate pi."

Roger Webster for the Bulletin of the LMS

"The judicious representative selection makes this a useful addition to one's library as a reference book, an enjoyable survey of developments and a source of elegant and deep mathematics of different eras."

Ed Barbeau for MathSciNet

"Full of useful formulas and ideas, it is a vast source of inspiration to any mathematician, A level and upwards—a necessity in any maths library."

New Scientist

"Should be on every mathematician’s coffee-table! … The seventy articles comprising the source-book proper range from historical articles and classic by such players as Wallis, Huyghens, Newton, and Euler, to the articles on irrationality and transcendence … . Pi: A source Book is truly an amazing book, irresistible in its own way, and filled with gems. And once it’s on your coffee-table, feel free to do more than just browse: it’s pretty well-suited for more in-depth study … . Obviously the book is highly recommended." (Michael Berg, MathDL, January, 2001)

From the reviews of the third edition:

"This is the third edition of the by now classical Pi: a source book. … contains some notes on the computation of individual (binary) digits of p, some considerations on the normality of the decimal expansion of p, and two more sections on the history of p. This book is still a classic work of reference for anyone with an interest in fascinating Pi.” (F. Beukers, Mathematical Reviews, 2005h)

"The book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein include selections from the mathematical and computational literature over four millennia, a variety of historical studies on the cultural significance of the number, and an assortment of anecdotal, fanciful, and simply amusing pieces." (Zentralblatt für Didaktik der Mathematik, November, 2004)

"This is the third edition of a comprehensive selection of about 70 articles on the number pi and related constants. … This edition contains a new supplement on the recent history of the computation of digits of pi … . Furthermore, new translations of articles by Viète and Huygens have been added. Altogether, this volume provides a fascinating overview of many hundred years of research and will delight and enlighten amateur lovers of pi and professional mathematicians alike." (Ch. Baxa, Monatshefte für Mathematik, Vol. 148 (1), 2006)

"This is a fascinating reference book, which consists almost entirely of facsimiles of 70 articles about pi, followed by appendices which look at its early history as well as much computational information. … it should be something to appear in any mathematical library, as it does contain so much material. … There is something for all levels of readers in this book, from the 14-year old who may wish to know a little of the history, to the professional mathematician seeking information … ." (Anthony C. Robin, The Mathematical Gazette, Vol. 90 (518), 2006)


Table of contents (70 chapters)

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

    Berggren, Lennart (et al.)

    Pages 1-2

  • Quadrature of the Circle in Ancient Egypt

    Engels, Hermann

    Pages 3-6

  • Measurement of a Circle

    Berggren, Lennart (et al.)

    Pages 7-14

  • Archimedes the Numerical Analyst

    Phillips, G. M.

    Pages 15-19

  • Circle Measurements in Ancient China

    Lay-Yong, Lam (et al.)

    Pages 20-35

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4757-3240-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Pi: A Source Book
Authors
Copyright
2000
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3240-5
DOI
10.1007/978-1-4757-3240-5
Edition Number
2
Number of Pages
XIX, 736
Number of Illustrations and Tables
25 b/w illustrations
Topics