Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges |
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Authors: | Károly J. Böröczky Salvador S. Gomis Péter Tick |
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Affiliation: | 1.Alfréd Rényi Institute of Mathematics,Budapest,Hungary;2.Roland E?tv?s University,Budapest,Hungary;3.University of Alicante,Alicante,Spain |
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Abstract: | For a given convex body K in with C 2 boundary, let P c n be the circumscribed polytope of minimal volume with at most n edges, and let P i n be the inscribed polytope of maximal volume with at most n edges. Besides presenting an asymptotic formula for the volume difference as n tends to infinity in both cases, we prove that the typical faces of P c n and P i n are asymptotically regular triangles and squares, respectively, in a suitable sense. Supported by OTKA grants 043520 and 049301, and by the EU Marie Curie grants Discconvgeo, Budalggeo and PHD. Authors’ addresses: Károly J. B?r?czky, Alfréd Rényi Institute of Mathematics, P.O. Box 127, Budapest H–1364, Hungary, and Department of Geometry, Roland E?tv?s University, Pázmány Péter sétány 1/C, Budapest 1117, Hungary; Salvador S. Gomis, Department of Mathematical Analysis, University of Alicante, 03080 Alicante, Spain; Péter Tick, Gyűrű utca 24, Budapest H–1039, Hungary |
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Keywords: | 2000 Mathematics Subject Classification: 52A27 52A40 |
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