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



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All the formulas of Pi


Reference of the On-Line Encyclopedia of Integer Sequences for Pi : A000796
Here is the most beautiful handbook of Pi formulas... Yes, believe me !

In the three following pages, you will find all the fomulas that propagated the legend of Pi. They're grouped by chronologic period or inspiration.

  • Geometry era (or inspired by Geometry)
    In a nutshell, all the formulas stemming from Archimedes' method.

  • Calculus era
    It's raining formulas ! Thanks to Euler in particular !

  • Modern era (XXth century)
    The best of the best... Hard to find in general, but exhilarating when digits begin to appear ! All of them except one are particular cases of the theory of modular equations

Image : extract from the Ramanujan's notebooks


Go to the page about mathematicians or follow the links provided in the above pages to find the authors and the proofs of these formulas