Anne Fontaine and Susan Hurley, Proof by picture: Products and reciprocals of diagonals length ratios in the regular polygon, Forum Geometricorum, 6 (2006) 97--101.

Abstract:  These ``proofs by picture'' link the geometry of the regular n-gon to formulae concerning the arithmetic of real cyclotomic fields. We illustrate the formula for the product of diagonal length ratios and that for the reciprocal of diagonal length ratio.

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