Hardcover
Published: 17th June 2004
ISBN: 9780387205717
Number Of Pages: 797
This 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.
For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, new translations of works by Viete and Huygen, as well as Kaplansky's never-before-published "Song of Pi."
From the reviews of earlier editions:
"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
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 fur 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 Viete 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 fur 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)
The Rhind mathematical papyrus-problem 50 (ca. 1650 B.C.) | p. 1 |
Engels : Quadrature of the circle in ancient Egypt (1977) | p. 3 |
Archimedes : Measurement of a circle (ca. 250 B.C.) | p. 7 |
Phillips : Archimedes the numerical analyst (1981) | p. 15 |
Lam and Ang : Circle measurements in ancient China (1986) | p. 20 |
The Banu Musa : the measurement of plane and solid figures (ca. 850) | p. 36 |
Madhava : The power series for Arctan and Pi (ca. 1400) | p. 45 |
Hope-Jones : Ludolph (or Ludolff or Lucius) van Ceulen (1938) | p. 51 |
Viete : Variorum de Rebus mathematicis reponsorum liber VII (1593) | p. 53 |
Wallis : Computation of [pi] by successive interpolations (1655) | p. 68 |
Wallis : Arithmetica infinitorum (1655) | p. 78 |
Huygens : De Circuli magnitudine inventa (1654) | p. 81 |
Gregory : correspondence with John Collins (1671) | p. 87 |
Roy : The discovery of the series formula for [pi] by Leibniz, Gregory, and Nilakantha (1990) | p. 92 |
Jones : The first use of [pi] for the circle ratio (1706) | p. 108 |
Newton : Of the method of fluxions and infinite series (1737) | p. 110 |
Euler : chapter 10 of Introduction to analysis of the infinite (on the use of the discovered fractions to sum infinite series) (1748) | p. 112 |
Lambert : Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) | p. 129 |
Lambert : Irrationality of [pi] (1969) | p. 141 |
Shanks : Contributions to mathematics comprising chiefly of the rectification of the circle to 607 places of decimals (1853) | p. 147 |
Hermite : Sur La Fonction Exponentielle (1873) | p. 162 |
Lindemann : Ueber die Zahl [pi] (1882) | p. 194 |
Weiserstrass : Zu Lindemann's Abhandlung "Uber die Ludolphsche Zahl" (1885) | p. 207 |
Hilbert : Ueber die Transzendenz der Zahlen e und [pi] (1893) | p. 226 |
Goodwin : Quadrature of the circle (1894) | p. 230 |
Edington : House bill no. 246, Indiana State Legislature, 1897 (1935) | p. 231 |
Singmaster : The legal values of Pi (1985) | p. 236 |
Ramanujan : Squaring the circle (1913) | p. 240 |
Ramanujan : Modular equations and approximations to [pi] (1914) | p. 241 |
Watson. The Aarquis and the land agent : a tale of the eighteenth century (1933) | |
Ballantine. The best (?) formula for computing [pi] to a thousand places (1939) | p. 271 |
Birch. An algorithm for construction of arctangent relations (1946) | p. 274 |
Niven. A simple proof that [pi] is irrational (1947) | p. 276 |
Reitwiesner. An ENLAC determination of [pi] and e to 2000 decimal places (1950) | p. 277 |
Schepler. The chronology of Pi (1950) | p. 282 |
Mahler. On the approximation of [pi] (1953) | p. 306 |
Wrench, Jr. the evolution of extended decimal approximations to [pi] (1960) | p. 319 |
Shanks and Wrench, Jr. calculation of [pi] to 100,000 decimals (1962) | p. 326 |
Sweeny. On the computation of Euler's constant (1963) | p. 350 |
Baker. Approximations to the logarithms of certain rational numbers (1964) | p. 359 |
Adams. Asymptotic diophantine approximations to e (1966) | p. 368 |
Mahler. Applications of some formulae by hermite to the approximations of exponentials of logarithms (1967) | p. 372 |
Eves. In mathematical circles; a selection of mathematical stories and anecdotes (excerpt) (1969) | p. 400 |
Eves. Mathematical circles revisited; a second collection of mathematical stories and anecdotes (excerpt) (1971) | p. 402 |
Todd. The lemniscate constants (1975) | p. 412 |
Salamin. Computation of [pi] using arithmetic-geometric mean (1976) | p. 418 |
Brent. Fast multiple-precision evaluation of elementary functions (1976) | p. 424 |
Beukers. A note on the irrationality of [Zeta](2) and [Zeta](3) (1979) | p. 434 |
Van der Poorten. A proof that Euler missed ... Apery's proof of the irrationality of [Zeta](3) (1979) | p. 439 |
Brent and McMillan. Some new algorithms for high-precision computation of Euler's constant (1980) | p. 448 |
Apostol. A proof that Euler missed : evaluating [zeta](2) the easy way (1983) | p. 456 |
O'Shaughnessy. Putting God back in math (1983) | p. 458 |
Stern. A remarkable approximation to [pi] (1985) | p. 460 |
Newman and Shanks. On a sequence arising in series for [pi] (1984) | p. 462 |
Cox. The arithmetic-geometric mean of gauss (1984) | p. 481 |
Borwein and Borwein. The arithmetic-geometric mean and fast computation of elementary functions (1984) | p. 537 |
Newman. A simplified version of the fast algorithms of Brent and Salamin (1984) | p. 553 |
Wagon. Is Pi normal? (1985) | p. 557 |
Keith. Circle digits : a self-referential story (1986) | p. 560 |
Bailey. The computation of [pi] to 29,360,000 decimal digits using Borwein's quartically convergent algorithm (1988) | p. 562 |
Kanada. Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of [pi] calculation (1988) | p. 576 |
Borwein and Borwein. Ramanujan and Pi (1988) | p. 588 |
Chudnovsky and Chudnovsky. Approximations and complex multiplication according to Ramanujan (1988) | p. 596 |
Borwein, Borwein and Bailey. Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi (1989) | p. 623 |
Borwein, Borwein and Dilcher. Pi, Euler numbers, and asymptotic expansions (1989) | p. 642 |
Beukers, Bezivin, and Robba. An alternative proof of the Lindemann-Weierstrass theorem (1990) | p. 649 |
Webster. The tale of Pi (1991) | p. 654 |
Eco. An except from Foucault's pendulum (1993) | p. 658 |
Keith. Pi mnemonics and the art of constrained writing (1996) | p. 659 |
Bailey, Borwein, and Plouffe. On the rapid computation of various polylogarithmic constraints (1997) | p. 663 |
On the early history of Pi | p. 677 |
A computational chronology of Pi | p. 683 |
Selected formulae for Pi | p. 686 |
Translations of Viete and Huygens | p. 690 |
A pamphlet on Pi | p. 721 |
Table of Contents provided by Blackwell. All Rights Reserved. |
ISBN: 9780387205717
ISBN-10: 0387205713
Audience:
Tertiary; University or College
Format:
Hardcover
Language:
English
Number Of Pages: 797
Published: 17th June 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 25.4 x 17.8
x 4.2
Weight (kg): 3.88
Edition Number: 3
Edition Type: Revised