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Isoperimetric inequality for non-Euclidean polygons (2409.06529v1)
Published 10 Sep 2024 in math.HO and math.MG
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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