Calculate Pi

There are lot of possibilities on how to calculate the circle number π:

Approximation
Continued Fraction

Approximation

Approximation after Archimedes

Archimedes was one of the first who tried to calculate Pi with approximation. He tried it with regular polygons and increased the number of corners to calculate an upper and lower limit for what Pi can be.
He calculated until the corner number 96 and came to the conclusion that Pi has to be lower than 3+(10/70) and higher than 3+(10/71)

Approximation after John Wallis (wallis product)

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Continued Fraction

Continued Fraction after Lord Brouncker

Continued Fraction after Johann Heinrich Lambert