My Math Forum polygon with 2^n vertices in a circle

 Algebra Pre-Algebra and Basic Algebra Math Forum

 December 19th, 2012, 05:48 PM #1 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 polygon with 2^n vertices in a circle The regular polygon (all sides are equal, all angles are equal) with $2^n$ vertices is inscribed into a circle. The radius of circle is R. The length of the side of this polygon is $a( 2^n )= R \cdot \sqrt{2- \underbrace_{ \; \; \; \; (n-2)}^{ \underbrace{\sqrt{2+ \sqrt{2+ ..... + \sqrt{2}} } } } }$ I used sine for solution but there are other ways also....

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