Pi Formulas, Algorithms and Computations
(Dec 31 2009)
2700 billion decimal digits of Pi computed with a desktop computer.
Formulas and Algorithms
(Jan 20 1997)
A new and faster formula to
compute the n'th binary digit of Pi. The article (Jan 20 1997) in html or in PDF
(revised edition, Feb 2007). A systematic way to find similar formulas is presented here.
(Jan 10 1997)
Simon Plouffe has
found an algorithm to compute the n'th digit of Pi in any base in
O(n^3log(n)^3) with little memory. We give here an improvement of his algorithm
to get a speed of O(n^2). The postscript file of the
of the article: pi_n2.ps
, the html
version, and the corresponding implementation in C: pi.c
(Feb 27 1997) A faster implementation which
uses the Gosper formula : pi1.c .
(Feb 4 1997)
While testing some numerical relations with the PSLQ
, I found this exotic formula for Pi:
(Aug 2003)Boris Gourevitch and Jesus Guillera
show how to demonstrate similar formulas.
Numbers, constants and computation, by Xavier Gourdon and Pascal Sebah
The Pi entry
in Wolfram MathWorld.
Jörg Arndt's home page .
Mathematical Constants from Steven Finch.
L'univers de Pi, by Boris
Simon Plouffe's home page .
A French book about Pi: Le
fascinant nombre Pi , Jean-Paul Delahaye, Editions Belin / Pour
La Science, Paris, 1997, ISSN 0224-5159 ISBN 2-9029-1825-9.
A German book about Pi by Jörg Arndt: Pi - Algorithmen,
Computer, Arithmetik, Springer-Verlag Heidelberg, ISBN 3-540-63419-3. English
translation to come.
Fabrice Bellard -