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

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

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Everything on Pi!

Since this site has for mission to inform each one of us on the profound and nearly mystic nature of Pi, nothing is worth more than a few articles or episodes to show that it is still modern and loved by current researcher and passionates.
Here is a list, yet once more incomplete, paper documents or video that I could find on the web. Due to time constraint, mess and laziness, I could not put everything I had. As always, if you see something new, tell me!

Digit records (html)

1000 billionth (10^12) binary digit of Pi by Fabrice Bellard- 22/09/97

5 000 billionth digit of Pi is '0' by Colin Percival (projet PiHex) - 21/08/98

40 000 billionth digit of Pi is '0' by Colin Percival (projet PiHex) - 9/02/99

The million billionth binary digit of Pi (1015) is '0' by Colin Percival (projet PiHex) - 11/09/00

51,539,600,000 decimals of Pi by Kanada

206,158,430,208 (=3*2^36) decimals of Pi by Kanada

Mathematical essays on

On the rapid computation of various polylogarithmic constants
Bailey - Borwein - Plouffe
pdf (1996)
(THE reference paper on Plouffe's formulaew)

Massive 3-loop Feynman diagrams reducible to SC primitives of algebras of the sixth root of unity
D. Broadhurst
pdf (10/03/98)
(The paper that naturally follow the previous one!)

Sur la nième décimale des nombres transcendants
ou La 10 milliardième décimale (hex) de Pi est 9

Simon Plouffe
pdf (1996)
English version (on the nth decimal of transcendant numbers or the 10 billionth decimal (hex) of Pi is 9)

Some BBP functions
Alexandru Lupas - Université de Sibiu (Roumanie)
dvi (2000)

The Computation of to 29,360,000 Decimal Digits using Borweins' Quartically Convergent Algorithm
David H. Bailey - Mathematics of Computation
pdf (21/04/87)

Pi: A 2000-Year Search Changes Direction
Victor Adamchik / Stan Wagon - Wolfram Research
pdf (23/09/97)

Spigot algorithm
mathcad 6 for pi

The Quest for Pi
David H. Bailey / Jonathan M. Borwein / Peter B. Borwein / Simon Plouffe
pdf (25/06/96)
(back on the algorithms and calculation record that marked history)

Approximations to Pi via the Dedekind eta function
Borwein - Garvan
postscript (27/03/96)

A new formula to compute the n'th binary digit of Pi
Fabrice Bellard
postscript (20/01/97)

Computation of the n'th digit of Pi in any base in O(n2)
Fabrice Bellard
postscript (10/01/97)

Evaluating Zêta(2)
Robin Chapman - Université d'Exeter
dvi (30/04/99)
(by BBP formulae)

Very cryptic stuff
Jörg Arndt - Chemnitz
(The details on Ramanujan formulae)

A new formula for Pi
M. Hirschhorn
postscript (05/12/97)
(a different proof of the Plouffe formula)

Construction d'un cercle et d'un carré de même aires (!!)
Construction of a circle and square with the same area(!!)
word format (1999)
(yes,yes, you di not misread, this boy thought he had prooved the squaring of a circle in another document.... each to their own! of course, his construction here is just an approximation, but a great geometrical exercise, for the amateurs....
I think he doesn't really understand the problem of rigour, since he was also telling me that Lindemann must have been wrong... a poet, this boy! I don't know wether he is a frustrated genius or a pasionate madman, or even both!)

Calculating Pi by Cues method
Christophe Borelly - IUT Béziers
pdf (03/01/00)

The amazing number Pi
Peter Borwein - CECM
pdf (07/2000)
(texte in honor of the rediscovery of the tomb of Ludolph van Ceulen)

Historic of the algorithm concerning Pi
P. Lorczak on mathsoft
mathcad 6 format

Formulae and algorithm to calculate Pi
Gérard Sookahet - Hutchinson
postscript format (08/2000)

Some article on Pi

Chaos in Pi
Hervé Poirier - Science et Vie n°1010 (Novembre 2001)
Here are the five pages with images, each 120 Kb: 1 - 2 - 3 - 4 - 5

Certirudes without proof
Jean Paul Delahaye - Pour La Science
pdf (07/98 n°249)
(really good article... thanks Abel Lacabanne for this great pdf)

The decimals of the number Pi
Hervé Morin - Le Monde
pdf (23/10/97)
(on the calculation by Fabrice Bellard)

System Pi - Contempary art exposition by François Morellet at the Musée Zadkine
html - Article de Libération (24/12/1999)

Two tasty servings of Pi
CMS Notes
pdf (11/98)
(Book review)

A passion for Pi
Ivars Peterson - Science News online
pdf (2/08/97)

Obsession of Pi
Jean-Paul Delahaye - Pour la science
pdf (01/97)

The mountains of Pi
Richard Preston - the New Yorker
html (02/03/1992)
(A long and remarquable article on the Chudnovsky brothers)

Presentations on Pi

The life of Pi - history and computation
Jonathan Borwein - Australian Colloquia
pdf (07/2003)
An excelent presentation that study the question under every angle with one of the best world specialist. A few pictures and a bit of humor as well.

Several students often have asked me for advise on presentation of Pi. I am happy to be able to reproduce their work that carry on their passion for Pi, and that will maybe be the beggining of a long fascination? The following presentations are in FRENCH, I'm waiting for your contributions in english !

Le nombre Pi (The number Pi)
DE GASPERIS Clément - FLOTTERER Mike - DOS SANTOS Steeve - ALRIC Christophe
Lycée Jacques BREL, Vénissieux - Supervised personal work - word format(2000)

Méthodes d'approximation du nombre Pi (Aprroximation Method for the number Pi)
PRZYBYLSKI Olivier - TIPE (prepa (undergraduate) exposition)
word format (2000)
(Lecturers' nightmare, with a name like that.... 150 points in Scrabble!!)

Comparaison des performances de différents algorithmes(Comparing the performance of different algorithm)
Xavier Marchesini - Ecole Centrale Paris
mathematica format (05/2000)

Le nombre Pi (The number Pi)
Laura Brichon - 6eme 2
word format(14/03/2000)

Mon séminaire de DEA consacré bien sûr à Pi...
(My DEA semester dedicated of course on Pi)...
format Word - PDF

Pi, le nombre diachronique (Pi, the diachronic number)
Bertrand Germain, Vincent Moreau, Antoine Riche, Yann Spadari - Licence mathématiques

Romain Dupont, Lynda Gastal - Licence de mathématiques
ps (31 pages, impresive!)

Tout Pi or not Tout Pi + frise chronologique
Elodie Lecocguen - Yessera Bdewi - TS
word (19 pages)

Le nombre Pi est-il naturel ? (Is the number Pi natural)
Antoine Taveneaux - Terminale S - travail de TPE (Pratical work)
PDF (38 pages)
Excelent work, focusing particularly on the apparitions of Pi in the world or the number that surround us. Loads of experiments.

Le nombre Pi (The number Pi)
Nicolas Hébrard, Sam Muth - MPSI - Travail de TIPE
PDF (24 pages)
Numerical approximation method. Nothing you won't find on this site ;-p Otherwise, not bad, detailled proof.

A few videos by Simon Plouffe

While waiting for the reopen of his site, here are the videos and sound extract that put him on scene about Pi.

Radio au Québec (Quebec Radio)
quicktime format (09/11/97) - 3.7Mo

Interview of Plouffe and the Borwein by NBC
quicktime format (23/11/96)
(great, 13.5 Mo)

The interview on RTL

As you know, for the follower of this site, RTL interviewed me on the 20 february 2000, in the Zikweb program. A great moment for me! Not to be missed, loud to Pi, and to my numerous "finally"!

RTL - ZikWeb program the 10/02/2000
"LE SITE OFFICIEL DU NOMBRE PI : 3,14 MOYENS DE DECOUVIR LES MATHEMATIQUES" ("the official site of the number Pi :3.14 ways to discover mathematics")

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