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Regular polygon approximation of $\pi$
01-19-2013, 05:30 PM
Post: #1
Regular polygon approximation of $\pi$

Let $A_n$ be the area of the inscribed regular polygon of unit circle (radius $=1$) with $n$ edges
while $P_n$ be the perimeter of the inscribed regular polygon of unit-dimeter circle.

The Fig below shows the beautiful relation $A_{2n} = P_n$, and the relation between $d_{2n}$ and $d_n$


This constitude the elegant procedure in $\pi$ approximation by ancient Chinese mathematician
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