A sharp lower bound on the polygonal isoperimetric deficit

TL;DR

This paper establishes a precise quantitative inequality that measures how far a polygon is from being optimal in the isoperimetric sense, providing a sharp lower bound on the polygonal isoperimetric deficit.

Contribution

It introduces a sharp lower bound for the polygonal isoperimetric deficit, advancing the understanding of polygon optimality in geometric inequalities.

Findings

Derived a sharp lower bound for the polygonal isoperimetric deficit

Quantified the deviation of polygons from optimal shape

Enhanced the theoretical understanding of polygonal isoperimetric inequalities

Abstract

A sharp quantitative polygonal isoperimetric inequality is obtained.