English

A Geometric proof for the Polygonal Isoperimetric Inequality

Metric Geometry 2023-09-13 v1

Abstract

Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area minimizing the perimeter must be regular.

Keywords

Cite

@article{arxiv.2309.05802,
  title  = {A Geometric proof for the Polygonal Isoperimetric Inequality},
  author = {Beniamin Bogosel},
  journal= {arXiv preprint arXiv:2309.05802},
  year   = {2023}
}
R2 v1 2026-06-28T12:18:36.913Z