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arXiv · 2409.06529

Isoperimetric inequality for non-Euclidean polygons

Basudeb Datta·Subhojoy Gupta
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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.

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Basudeb Datta, Subhojoy Gupta. 2024-09-10. Isoperimetric inequality for non-Euclidean polygons. https://arxiv.org/abs/2409.06529

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