Journal for Geometry and Graphics 29 (2025), No. 2, 267--275
Copyright by the authors licensed under CC BY SA 4.0
Tangential n-gons with Commensurability Conditions
Giuseppina Anatriello
Dipartimento di Architettura, Università degli Studi di Napoli, Italy
anatriello@unina.it
Silvano Rossetto
Centro Morin, Pieve del Grappa, Italy
rossetto49@gmail.com
Giovanni Vincenzi
Dipartimento di Matematica, Università di Salerno, Fisciano, Italy
vincenzi@unisa.it
Each regular polygon P is clearly tangential, has commensurable sides and every choice of three consecutive vertices among those of P determines a triangle whose interior angles are pairwise commensurable. In this article we prove that these three conditions are also sufficient for a convex polygon to be equilateral. This leads to a new characterization of convex regular polygons with an odd number of sides.
Keywords: Tangential polygon, equilateral polygon, incommensurability, regular polygon.
MSC: 51M40; 97G40, 97D80.
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