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For most purposes, knowing the value of Pi to two decimal places is enough. In a few practical applications, someone may need to know the ratio to 10 or 15 decimal places, but rarely more. Thirty-nine decimal places suffice for computing the circumference of a circle enclosing the known universe with an error no greater than the radius of a hydrogen atom.

Here are famous formulations and approximations for Pi:

Newton's approximation of Pi

Pi approximated using Leonhard Euler's sums

Simple derivations for Pi

Other Formulas

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