Download Pi: The Next Generation: A Sourcebook on the Recent History by David H. Bailey,Jonathan M. Borwein PDF

By David H. Bailey,Jonathan M. Borwein

This publication includes a compendium of 25 papers released because the Nineteen Seventies facing pi and linked issues of arithmetic and laptop science.  the gathering starts with a Foreword through Bruce Berndt. every one contribution is preceded through a quick precis of its content material in addition to a quick key thesaurus indicating how the content material pertains to others within the assortment. the amount comprises articles on real computations of pi, articles on mathematical questions on the topic of pi (e.g., “Is pi normal?”), articles proposing new and sometimes remarkable thoughts for computing digits of pi (e.g., the “BBP” set of rules for pi, which allows one to compute an arbitrary binary digit of pi with no need to compute any of the digits that got here before), papers offering vital primary mathematical effects when it comes to pi, and papers featuring new, high-tech suggestions for interpreting pi (i.e., new graphical innovations that let one to visually see if pi and different numbers are “normal”).  

This quantity is a spouse to Pi: A resource Book whose 3rd version published in 2004.  the current assortment starts off with 2 papers from 1976, released through Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and different simple mathematical capabilities, derived from a few mathematical paintings of Gauss. Bailey and Borwein carry that those papers represent the start of the fashionable period of computational mathematics.  this period of time (1970s) additionally corresponds with the creation of high-performance computers (supercomputers), which seeing that that point have elevated relentlessly in strength, through nearly an element of 100,000,000, advancing approximately on the related expense as Moore’s legislation of semiconductor know-how.  This e-book will be of curiosity to quite a lot of mathematical readers; a few articles hide extra complicated examine questions compatible for energetic researchers within the field, but numerous are hugely obtainable to undergraduate arithmetic students.

Show description

Read or Download Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its Computation PDF

Similar number theory books

Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads

The ebook presents a self-contained creation to classical Number concept. all of the proofs of the person theorems and the suggestions of the routines are being provided step-by-step. a few historic comments also are offered. The e-book could be directed to complicated undergraduate, starting graduate scholars in addition to to scholars who organize for mathematical competitions (ex.

Elementary Dirichlet Series and Modular Forms (Springer Monographs in Mathematics)

A e-book on any mathematical topic past the textbook point is of little worth until it comprises new rules and new views. It is helping to incorporate new effects, only if they offer the reader new insights and are offered besides recognized outdated leads to a transparent exposition. it really is with this philosophy that the writer writes this quantity.

Zeta and eta functions: A new hypothesis

Euler-Riemann’s zeta and Dirichlet’s eta capabilities are outlined for genuine destructive numbers as analytic continuation. within the current ebook the writer defines new sequence for zeta and eta features, for genuine unfavorable and imaginary numbers with out analytic continuation. the hot zeta and eta capabilities retain the nature of harmonic sequence and alternating harmonic sequence respectively for actual adverse numbers, as for genuine confident numbers.

Computation with Linear Algebraic Groups (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Designed as a self-contained account of a few key algorithmic difficulties and their ideas for linear algebraic teams, this ebook combines in a single unmarried textual content either an advent to the elemental idea of linear algebraic teams and a considerable selection of invaluable algorithms. Computation with Linear Algebraic teams bargains a useful advisor to graduate scholars and researchers operating in algebraic teams, computational algebraic geometry, and computational staff conception, in addition to these trying to find a concise advent to the speculation of linear algebraic teams.

Extra info for Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its Computation

Sample text

Download PDF sample

Rated 4.55 of 5 – based on 26 votes