Pi: The Next Generation A Sourcebook on the Recent History of Pi and Its Computation /

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 in...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bailey, David H. (Autor), Borwein, Jonathan M. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Temas:
Mathematics-Data processing.
Number theory.
Mathematics.
History.
Computational Mathematics and Numerical Analysis.
Number Theory.
History of Mathematical Sciences.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Foreword
  • Preface
  • Introduction
  • Computation of pi using arithmetic-geometric mean
  • Fast multiple-precision evaluation of elementary functions
  • The arithmetic-geometric mean of Gauss
  • The arithmetic-geometric 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 arithmetic-geometric mean, ellipses, pi, and the ladies diary
  • Vectorization of multiple-precision 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.

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