All formulas
Num. approx.
Misc. math.
Delirium !

Boris Gourévitch
The world of Pi - V2.57
modif. 13/04/2013

Pi-Day in
Pi Day Countdown
Home Version history Guestbook Who I am Some pictures (fr) Acknowledgements Last modifications Contact

Cette page en français This page in English

Hello everyone !

 Finally, this French website has been translated into English !! Yeahhh ! Many many thanks to Florian Bouyer (first prize), David Jelgersma, Guillaume (Bobest3g), Thomas Robitaille and myself ;-). Since some (all) of these translators were not English-native speakers, I have to ask you to be VERY tolerant regarding the quality of English. If you have time and if you like these pages, any help to correct the English would be very much appreciated, please contact me.

Also, be aware that 50% of the content of pi314.net is more than 10-years old, at a time when the web was still mostly in version 1.0 and when Google had just achieved its first round of equity funding. Thus, this website has to do neither with advanced interfaces nor with blogging, twittering, facebook, Wikipedia or others social modern ideas. Pi314.net is just a personalized collection of 170 pages about the most wonderful number in the universe (to me... no, it really is): Pi. In other words, let's forget about the soulless Pi's page of Wikipedia !! :-) (ok, all right, I like it all the same but it's depressive, isn't it ?)

In this website, you will find here and there some numbers like Axxxxxx which refer to the great website of Neil Sloane : Encyclopedia of Integer Sequences. For instance, you can find Pi's digits here A000796.

Finally, Pi Lovers are encouraged to write and propose new pages on Pi ! Most recent ones by myself have been written using a LaTeX template ( LaTeX template, LyX 1.3 template, about LyX) then converted by Tex4ht from LaTeX to HTML. Thus, in a nutshell, you can send me a LaTeX file with something nice or fun about Pi and roughly following the above template and I will include it in the website (with your name of course) after having converted it. See for instance a page from a great guy with lots of good ideas.


Pi news !

Jonathan Borwein passed away suddenly on August 2nd, 2016, at 65... :-( He was the father of experimental mathematics and he showed a deep interest into Pi as shown on his page... This is really a great loss for the community !


Remember that in december 2009, Fabrice Bellard broke a new Pi-record: the greatest number of digits computed on a personal computer (2700 billions !!). See here the details about this wonderful record ! Well, this record was broke by Alexander J. Yee & Shigeru Kondo on 2010, august 2nd with 5000 billions ! See here the announce and here for details. Well, as a personel computer, it is a monster (see on right) with 12 cores, 96GB of memory and 39TB of hard drive storage. Not exactly the personal computer of everyone...


I still can't believe it but I finally published a research paper on Pi with Jesús Guillera ! :
Construction of binomial sums for π and polylogarithmic constants inspired by BBP formulas, Appl. Math. E-Notes, 7(2007), 237-246.

News of the website

- I'm looking for people correcting and improving the english on this website. If you like this website and even have a few minutes, thank you in advance for your help.

  • Again, a new algorithm from Benoit Cloitre in an Archimedes fashion !!
  • A new algorithm from Benoit Cloitre in a continued fraction fashion
  • New pages Links, Bibliography and Poems entirely as databases. Thus, you can leave comments and propose your own poems, links or books !

Who are you, dear visitor ?? (11695 votes from a previous poll)

A mathematician (don't be modest) (1519) 13.0%
An undergraduate in maths (2283) 19.5%
Well, say, I just like maths (2132) 18.2%
I'm in high school (2069) 17.7%
Pi and its legend are fun to me (1700) 14.5%
My hobby is more about history, computer programming or music... (470) 4.0%
A web-addict, that's all (650) 5.6%
I just ran into this website unexpectedly (514) 4.4%
Ooops, this is not where I wanted to arrive ! (358) 3.1%


If this is the first time you're visiting (or even if you're used to come !) it is possible that you are confused with my messy website... Innovation (absolutely...), I made a sitemap available in order to access the wanted webpage quickly ! If you're looking for a given word, do not hesitate to use the search engine at the top of this window

Around the website
Version history/news (Pi, site, me)    
Column Whenever I have time, some personal thoughts (likely in french)
Pages in .pdf Get pages from the website  
Who I am      
Some pictures The narcissistic page  
Nets d'or fifteen minutes of glory (in french)  
Cited in      
Last changes    
History of Pi of course !
Al Kashi Geometry  
Archimedes Geometry  
Bellard BBP Formula  
J. and P.Borwein Ultra fast Algos -Ramanujan's formulas
Brounker Continued Fractions  
Brown Number theory  
Buffon Needle's problem, probabilities  
G. et D. Chudnovsky Ramanujan's like formulas  
Cesaro Probabilities  
Cues Geometry  
Descartes Geometry  
Estenave/Fretigny Sums. Residuals theorem.
Euler Sums  
Fibonacci Fibonacci sequence  
Fourier How to prove Euler's sums
Gauss Machin like formula  
Gosper Strange sums and formulas
Huvent Hypergeometric sums
Katahiro Geometry  
Lambert   Pi is irrational  
Leibniz   A simple sum  
Lindemann   Pi is a transcendental number  
Machin   A famous sum  
Mandelbrot/Bolle/Edgar Fractals and Pi  
Moivre/Stirling Stirling's formula  
Newton   Inverse sinus sum  
Plouffe   BBP formulas  
Ramanujan Incredible formulas  
Salamin/Brent Ultra-fast algorithm  
Viete   Geometry  
Wallis   Infinite product  
Woon   Formula  
All formulas    
Geometry-based Antiquité - 16e siècle  
Analysis-based 17e siècle - 19e siècle  
Modern algorithms 20e siècle  
Numerical approximations    
PiFast 3.2      
Classes Java    
Misc and personal formulas    
Lots of formulas !    
Hypergeometrical sums  
Randomness-related phenomena Probability theorems, Brownian motion
Complexity Normal numbers, randomness
Pi's digits and statistics Fractal dimension, tests on digits, Khintchin's constant
Personal ideas BBP sums
Chebychev's polynomials Sums
Spigot's algorithm How to compute Pi digits by hand
The Attic   Mixture of unexpected formulas for Pi
C(n,k) Triangle Counting
Arithmetic functions Gauss, Euler, Moëbius, Zeta
New stuff with old stuff ! Improvement of Archimede's formula. By Benoît Cloitre
A Xmas formula for Pi by Benoit Cloitre
e and Pi in a mirror Two symetrical formulas for e and Pi ! by Benoit Cloitre
Pi and Log(2) in a mirror Two continued fractions for Pi and Log(2) by Benoit Cloitre
Maths definitions    
Bernoulli's numbers  
Methods used in Pi digits computing
Aitken's Delta2 Fasten formulas
Newton's algorithm Extract roots
n-th digit of a number How to use BBP formulas
Fast Fourier transform How to multiply two large integers efficiently
Computation records    
Graph of records    
n-th digit record (base 2) Use of BBP formulas  
Continued fractions    
Memory of digits    
Records announcements    
Record 04/99 (68m) Details on the record  
Record 09/99 (206m) same  
Record 12/2002 (1241m) same  
Statistics on Pi's digits Frequency of digits  
1m digits: text (HTML) 1 million digits  
Download (stuffit) 1 million digits  
Download (zip) 1 million digits  
The world of Pi
Poems   Poems on or from Pi  
Research papers    
Papers from magazines    
Videos Simon Plouffe    
Interview RTL (french)    
Delirium !      
Anecdotes about mathematicians  
Anecdotes about Pi    
Short Pi quizz Test your knowledge about Pi
Tough Pi quizz Same  
How many digits do you know ?  
 Pi-day International day of Pi !  
Images/Wallpapers About Pi of course  
Music Pi in music    
Links about Pi      
Bibliography Books to have  

Vote for this website ! Hit-Parade

Already Pi-lovers have come on this website since 06/20/99 !

Boris Gourévitch / CNPS Lab, CNRS, Université of Orsay, Paris XI, France

The World of Pi - Version 2.57
Updated 13/04/2013

* Last changes :
Some stuff for Piday 2013 - Digits in a classroom - Update of the Piday Page - The English version !! Everything is new in english ;-)
* Coming next:
Many corrections in english and updates of links, biblio, poems, music and so on...

The Pi Web Ring™

This The Pi Web Ring site owned by Boris GOUREVITCH.
[Previous 5 Sites|Previous|Next|Next 5 Sites|Random Site|List Sites|Join]

Next Site

Site of the day on Télérama , August 20th, 2002

Interview in "Clicomédie" (RIP), TV program on France 2, January 30th, video here (8Mo, in french), and French newspaper Ouest France

Interviewed in Radio program Zikweb from RTL on february 10th, 2000. Here is the MP3 in french

Website of the week on september 5th, 1999 on Franco-Science (RIP)

Page of the day in l'actualité du Net, section sciences, 07/08/99

et personal website of the day, 07/07/99 on Interneto

Some other (pretty old !) awards

Tracking par Google Analytics