Isoperimetric inequality for non-Euclidean polygons
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909310781489152 |
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| author | Datta, Basudeb Gupta, Subhojoy |
| author_facet | Datta, Basudeb Gupta, Subhojoy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isoperimetric inequality for non-Euclidean polygons Datta, Basudeb Gupta, Subhojoy History and Overview Metric Geometry 52A10, 52A38, 52A55 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. |
| title | Isoperimetric inequality for non-Euclidean polygons |
| topic | History and Overview Metric Geometry 52A10, 52A38, 52A55 |
| url | https://arxiv.org/abs/2409.06529 |