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## Details

Material Type: | Manuscript, Internet resource |
---|---|

Document Type: | Book, Archival Material, Internet Resource |

All Authors / Contributors: |
Lennart Berggren; Jonathan M Borwein; Peter B Borwein |

ISBN: | 0387205713 9780387205717 9781441919151 1441919155 |

OCLC Number: | 53814116 |

Description: | xix, 797 p. : ill. ; 27 cm. |

Contents: | Preface. -- Acknowledgments. -- Introduction. -- The Rhind mathematical papyrus-problem 50 ( ̃1650 B.C.). -- Engles. Quadrature of the circle in ancient Egypt (1977). -- Archimedes. Measurement of a circle ( ̃250 B.C.). -- Phillips. Archimedes the numerical analyst (1981). -- Lam and Ang. Circle measurements in ancient China (1986). -- The Banū Mūsā: the measurement of plane and solid figures ( ̃850). -- Mādhava. The power series for Arctan and Pi ( ̃1400). -- Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938). -- Viète. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593). -- Wallis. Computation of Pi by successive interpolations (1655). -- Wallis. Arithmetica Infinitorum (1655).- Huygens. De Circuli Magnitudine Inventa (1654). -- Gregory. Correspondence with John Collins (1671). -- Roy. The discovery of the series formula for Pi by Leibniz, Gregory, and Nilakantha (1990). -- Jones. The first use of Pi for the circle ratio (1706). -- Newton. Of the method of fluxions and infinite series (1737). -- Euler. Chapter 10 of "Introduction to analysis of the infinite" (On the use of the discovered fractions to sum infinite series) (1748). -- Lambert. Mémoire Sur Quelques Proprietés Remarquables Des Quantités Transcendentes Circulaires et Logarithmiques (1761).- Lambert. Irrationality of Pi (1969). -- Shanks. Contributions to mathematics comprising chiefly of the rectification of the circle to 607 places of decimals (1853). -- Hermite. Sur La Fonction Exponentielle (1873). -- Lindemann. Ueber die Zahl Pi (1882). -- Weierstrass. Zu Lindemann's Abhandlung "Über die Ludolphsche Zahl" (1885). -- Hilbert. Ueber die Transzendenz der Zahlen e und Pi (1893). -- Goodwin. Quadrature of the circle (1894). -- Edington. House bill no. 246, Indiana State Legislature, 1897 (1935). -- Singmaster. The legal values of Pi (1985). -- Ramanujan. Squaring the circle (1913). -- Ramanujan. Modular equations and approximations to Pi (1914). -- Watson. The Marquis and the land agent: a tale of the Eighteenth Century (1933). -- Ballantine. The best(?) formula for computing Pi to a thousand places (1939). -- Birch. An algorithm for construction of arctangent relations (1946). -- Niven. A simple proof that Pi is irrational (1947). -- Reitwiesner. An ENIAC determination of Pi and e to 2000 decimal places (1950). -- Schepler. The chronology of Pi (1950). -- Mahler. On the approximation of Pi (1953). -- Wrench, Jr. The evolution of extended decimal approximations to Pi (1960). -- Shanks and Wrench, Jr. Calculation of Pi to 100,000 decimals (1962). -- Sweeny. On the computation of Euler's constant (1963). -- Baker. Approximations to the logarithms of certain rational numbers (1964). -- Adams. Asymptotic diophantine approximations to e (1966). -- Mahler. Applications of some formulae by Hermite to the approximations of exponentials of logarithms (1967). -- Eves. In mathematical circles; a selection of mathematical stories and anecdotes (excerpt) (1969). -- Eves. Mathematical circles revisited; a second collection of mathematical stories and anecdotes (excerpt) (1971). -- Todd. The Lemniscate constants (1975). -- Salamin. Computation of Pi using arithmetic-geometric mean (1976). --Brent. Fast multiple-precision evaluation of elementary functions (1976). -- Beukers. A note on the irrationality of [Apéry's constant](2) and [Apéry's constant](3) (1979). -- van der Poorten. A proof that Euler missed... Apéry's proof of the irrationality of [Apéry's constant](3) (1979). -- Brent and McMillan. Some new algorithms for high-precision computation of Euler's constant (1980). -- Apostol. A proof that Euler missed: evaluating [Apéry's constant](2) the easy way (1983). -- O'Shaughnessy. Putting God back in math (1983). -- Stern. A remarkable approximation to Pi (1985). -- Newman and Shanks. On a sequence arising in series for Pi (1984). -- Cox. The arithmetic-geometric mean of Gauss (1984). -- Borwein and Borwein. The arithmetic-geometric mean and fast computation of elementary functions (1984). -- Newman. A simplified version of the fast algorithms of Brent and Salamin (1984). -- Wagon. Is Pi normal? (1985). -- Keith. Circle digits: a self-referential story (1986). -- Bailey. The computation of Pi to 29,360,000 decimal digits using Borwein's quartically convergent algorithm (1988). -- Kanada. Vectorization of multiple-precision arithmetic program and 201,326, 000 decimal digits of Pi calculation (1988). -- Borwein and Borwein. Ramanujan and Pi (1988). -- Chudnovsky and Chudnovsky. Approximations and complex multiplication according to Ramanujan (1988). -- Borwein, Borwein and Bailey. Ramanujan, modular equations, and approximations to Pi or How to compute one billion digits of Pi (1989). -- Borwein, Borwein and Dilcher. Pi, Euler numbers and asymptotic expansions (1989). -- Beukers, Bezivin, and Robba. An alternative proof of the Lindemann-Weierstrass theorem (1990). -- Webster. The tale of Pi (1991). -- Eco. An excerpt from Foucault's Pendulum (1993). -- Keith. Pi mnemonics and the art of constrained writing (1996). -- Bailey, Borwein, and Plouffe. On the rapid computation of various polylogarithmic constants (1997). |

Other Titles: | Pi |

Responsibility: | [edited by] Lennart Berggren, Jonathan Borwein, Peter Borwein. |

More information: |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

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) Read more...

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