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Continued fraction for pi

A continued fraction for the number π = 3,1415… is



We will start with the development of

By substituting  in Euler's formula you get


Substitution of z = i in the continued fraction for the logarithm then gives

and because i 2 = – 1 you get



In his book Aritmetica infinitorum the English mathematician John Wallis described in 1665 this formula.

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