A Geometric proof for the Polygonal Isoperimetric Inequality

2023/09/11 by Beniamin Bogosel, Bogosel, Beniamin
Mathematics · Engineering · #Mathematics and Applications #Robotic Mechanisms and Dynamics #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2309.05802

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.

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