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Euler's formula for pi

You can calculate the value of π = 3.1415… with the formula that Leonhard Euler developed

 


Explanation

For an angle of 45˚ applies

and the inverse tangent is

Substitution in the power series for the inverse tangent gives

It converges too slowly to be able to use in practice.

This is one of the simplest calculations of π.

 


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