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A characterization of regular \(n\)-gons whose pairs of diagonals are either congruent or incommensurable. (English) Zbl 1451.11065

Let \(P_n\) be a regular \(n\)-gon. The authors prove that all pairs of diagonals of \(P_n\) are either congruent or incommensurable if and only if \(6\) does not divide \(n\). This gives that the question of incommensurability of diagonals of regular polygons is reduced to cases in which the number of sides of the regular polygon is a multiple of \(6\).

MSC:

11H99 Geometry of numbers
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