The First Exact Formula for ∏

Byoopstart

The First Exact Formula for \pi was by an Indian mathematician, Madhava of Sangamagrama, who discovered the Maclaurin series for arctangent in the 14th century:

    \[\pi=4\left(1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+...\right)\]

Nowadays this is know as the Madhava-Leibniz formula. Madhava also found another formula based on \pi=6arctan(1/\sqrt{3}):

    \[\pi=\sqrt{12}\left(1-\frac{3}{3\cdot3}+\frac{3}{5\cdot3^2}-\frac{3}{7\cdot3^3}+...\right)\]

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