Isoperimetric inequality for non-Euclidean polygons
History and Overview
2024-09-11 v1 Metric Geometry
Abstract
It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this note, we present a complete proof of this polygonal isoperimetric inequality in hyperbolic and spherical geometries.
Keywords
Cite
@article{arxiv.2409.06529,
title = {Isoperimetric inequality for non-Euclidean polygons},
author = {Basudeb Datta and Subhojoy Gupta},
journal= {arXiv preprint arXiv:2409.06529},
year = {2024}
}
Comments
8 pages, 6 figures