A regular polygon of n sides is inscribed in a circle of unit diameter. Show that its

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A regular polygon of n sides is inscribed in a circle of unit diameter. Show that its perimeter pn is given by

I Pn=nsin- n

Using the series expansion for sine, prove that

= Pn+ and deduce that  1 3! n S 1 5! n 1  = -(4P2n - Pn) +- 3 1  5 1 4 5! n +...

Given p12 = 3.1058 and p24 = 3.1326, use this result to obtain a better estimate of π.

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