Product of Chord Lengths Wall Art Poster

Inscribe a regular \(17\)-gon in a circle of radius \(1\). Fix one vertex, and draw the chords from that vertex to each of the others. The product of those chords' lengths is \(17\), the number of sides! The same is true for any number \(n\) of sides greater than \(1\). The proof in the image uses precalculus-level algebra, and properties of complex numbers: How a monic polynomial (whose top-degree coefficient is \(1\)) factors in terms of its roots, and the way a difference of \(n\)-th powers factors.

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