Perimeter approximation of convex discs in the hyperbolic plane and on the sphere
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866914461867048960 |
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| author | Fodor, Ferenc |
| author_facet | Fodor, Ferenc |
| contents | Eggleston (1957) proved that in the Euclidean plane the best approximating convex $n$-gon to a convex disc $K$ is always inscribed in $K$ if we measure the distance by perimeter deviation. We prove that the analogue of Eggleston's statement holds in the hyperbolic plane, and we give an example showing that it fails on the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_03655 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Perimeter approximation of convex discs in the hyperbolic plane and on the sphere Fodor, Ferenc Metric Geometry 52A55, 52A27, 52A40 Eggleston (1957) proved that in the Euclidean plane the best approximating convex $n$-gon to a convex disc $K$ is always inscribed in $K$ if we measure the distance by perimeter deviation. We prove that the analogue of Eggleston's statement holds in the hyperbolic plane, and we give an example showing that it fails on the sphere. |
| title | Perimeter approximation of convex discs in the hyperbolic plane and on the sphere |
| topic | Metric Geometry 52A55, 52A27, 52A40 |
| url | https://arxiv.org/abs/1902.03655 |