Typical faces of best approximating polytopes with a restricted number of edges
Let K be a convex body in E3 with a C2 smooth boundary. In this article, we investigate polytopes with at most n edges circumscribed about K or inscribed in K, which approximate K best in the Hausdorff metric. The asymptotic behaviour of the distance, as a function of n, of such best approximating...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16304 |
| Tartalmi kivonat: | Let K be a convex body in E3 with a C2 smooth boundary. In this article, we investigate polytopes with at most n edges circumscribed about K or inscribed in K, which approximate K best in the Hausdorff metric. The asymptotic behaviour of the distance, as a function of n, of such best approximating polytopes and K is known, see [3] for an asymptotic formula. In this article, we prove that the typical faces of the best approximating circumscribed or inscribed polytopes in the Hausdorff metric with at most n edges are asymptotically squares with respect to the second fundamental form of dK. |
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| Terjedelem/Fizikai jellemzők: | 313-327 |
| ISSN: | 0001-6969 |