Canvas: Product of Chord Lengths

Description

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.

EU representative: HONSON VENTURES LIMITED, gpsr@honsonventures.com, 3, Gnaftis House flat 102, Limassol, Mesa Geitonia, 4003, CY

Product information: Generic brand, 2 year warranty in EU and Northern Ireland as per Directive 1999/44/EC

Care instructions: If the canvas does gather any dust, you may wipe it off gently with a clean, damp cloth.