Pi : the next generation : a sourcebook on the recent history of Pi and its computation
 Responsibility
 David H. Bailey, Jonathan M. Borwein.
 Publication
 Switzerland : Springer, 2016.
 Physical description
 1 online resource (xiv, 507 pages)
Online
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Description
Creators/Contributors
 Author/Creator
 Bailey, David H., author.
 Contributor
 Borwein, Jonathan M., author.
Contents/Summary
 Contents

 Foreword
 Preface
 Introduction
 Computation of pi using arithmeticgeometric mean
 Fast multipleprecision evaluation of elementary functions
 The arithmeticgeometric mean of Gauss
 The arithmeticgeometric mean and fast computation of elementary functions
 A simplified version of the fast algorithms of Brent and Salamin
 Is pi normal?
 The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm
 Gauss, Landen, Ramanujan, the arithmeticgeometric mean, ellipses, pi, and the ladies diary
 Vectorization of multipleprecision arithmetic program and 201,326,000 decimal digits of pi calculation.Ramanujan and pi
 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi
 Pi, Euler numbers, and asymptotic expansions
 A spigot algorithm for the digits of pi
 On the rapid computation of various polylogarithmic constants
 Similarities in irrationality proofs for pi, ln 2, ?(2), and?(3)
 Unbounded spigot algorithms for the digits of pi
 Mathematics by experiment: Plausible reasoning in the 21st century
 Approximations to pi derived from integrals with nonnegative integrands
 Ramanujan's series for 1/?: A survey
 The computation of previously inaccessible digits of?2 and Catalan's constant
 Walking on real numbers
 Birth, growth and computation of pi to ten trillion digits
 Pi day is upon us again and we still do not know if pi is normal
 The Life of pi
 I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly
 Bibliography
 Index.
 Foreword
 Preface
 Introduction
 Computation of pi using arithmeticgeometric mean
 Fast multipleprecision evaluation of elementary functions
 The arithmeticgeometric mean of Gauss
 The arithmeticgeometric mean and fast computation of elementary functions
 A simplified version of the fast algorithms of Brent and Salamin
 Is pi normal The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm
 Gauss, Landen, Ramanujan, the arithmeticgeometric mean, ellipses, pi, and the ladies diary
 Vectorization of multipleprecision arithmetic program and 201,326,000 decimal digits of pi calculation.Ramanujan and pi
 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi
 Pi, Euler numbers, and asymptotic expansions
 A spigot algorithm for the digits of pi
 On the rapid computation of various polylogarithmic constants
 Similarities in irrationality proofs for pi, ln 2, ζ(2), and ζ(3)
 Unbounded spigot algorithms for the digits of pi
 Mathematics by experiment: Plausible reasoning in the 21st century
 Approximations to pi derived from integrals with nonnegative integrands
 Ramanujan's series for 1/π: A survey
 The computation of previously inaccessible digits of π2 and Catalan's constant
 Walking on real numbers
 Birth, growth and computation of pi to ten trillion digits
 Pi day is upon us again and we still do not know if pi is normal
 The Life of pi
 I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly
 Bibliography
 Index.
 Summary
 This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., ℓ́ℓIs pi normal?ℓ́ℓ), articles presenting new and often amazing techniques for computing digits of pi (e.g., the ℓ́ℓBBPℓ́ℓ algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, hightech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are ℓ́ℓnormalℓ́ℓ). his volume="" is="" a="" companion="" to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe ℓ́ℓquadratically convergentℓ́ℓ algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of highperformance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Mooreℓ́ℓs Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.
Subjects
Bibliographic information
 Publication date
 2016
 Note
 Includes index.
 ISBN
 9783319323770 (electronic bk.)
 3319323776 (electronic bk.)
 331932375X (print)
 9783319323756 (print)
 9783319323756 (print)
 DOI
 10.1007/9783319323770