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



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Miscellaneous mathematics / personal and anonymous formulas


Reference of the On-Line Encyclopedia of Integer Sequences for Pi digits: A000796

Plenty of formulas !

This is the odds and ends of mathematical formulas !
Actually, I gathered here the stuff that was difficult to put somewhere else. Some personal stuff at first, often related to Plouffe formulas. Then, some formulas of unknown origin, which use very interesting methods though. Finally, I present some useful methods for computation of pi digits.

  • Pi and randomness
    Several things to discuss and three pages
    1. How Pi appears in the random phenomenon
      Probabilistic theorems, Brownian Motion...
    2. Pi and the definitions of randomness theory
      Normal numbers, random sequences of Martin-Löf, computational complexity theory, BBP formulas...
    3. Statistical properties of Pi digits
      Fractal dimension, tests on digits, Khintchine constant...


  • Some personal ideas of formulas for Pi
    BBP formulas...

  • Chebychev polynomials
    a very personal idea to generate some BBP-like formulas with the Chebychev polynomials !

  • Spigot algorithm
    A recent and original method to compute the digits of Pi by hand, one after the other

  • My old page Attic
    A potpourri of apparitions of Pi in some mathematical problems. Hope I'll renovate this page one day...

  • C(n,k) Triangle
    A nice study about an integer triangle (like Pascal triangle) and which gives an approximation of Pi, of course ! This page definitely deserved to be taken out of the attic !

  • Arithmetic functions and Pi
    Gauss, Euler and Moëbius functions, and several relations with Zeta function, for instance


  • e and Pi in a mirror
    A beautiful brainwave of Benoit Cloitre about the similarity between two algorithms converging towards these two constants
Mathematical definitions

Visit the page about mathematicians to find pages related to these tools, or follow the links provided in the above pages