Published Paper

Inserted: 16 apr 2026
Last Updated: 16 apr 2026

Journal: The American Mathematical Monthly
Volume: 132
Number: 7
Pages: 666-675
Year: 2025

Abstract:

Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in the literature involving other shape functionals as well as further open problems.