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



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Formulas giving Pi
based on geometrical methods
(by chronological order of authors or people who inspired them)


Archimède : (287 AVJC - 212 AVJC)

Fibonacci : (1180 - 1250)

Geometrical application of the Fibonacci's suite :

U0 and U1 being strictly positive, (if equal to 1, it is the Fibonacci's suite !),

e


With e the golden number, e

Al Kashi : (? - 1429)

De Cues : (1401 - 1464)

Viete : (1540 - 1603)

              

Descartes : (1596 - 1650)

Wallis : (1616 - 1703)





(the third one is just an improved version of the second one)


Other formulas : (see the Attic )

1)

2) Small formula on my own



3) Application of the law of large numbers


Let  be a random sequence of n points in the square [0,1]x[0,1] and Dn the size of the set of these points in the circle of center 0 and radius 1, i.e.  , then  .

4) Isolated sequence

e



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