Abstract
The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space E n is at most n + 2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in E n and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C. In general, this ratio cannot be improved, as it follows from the example of any double-cone.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Lassak, M. Approximation of convex bodies by inscribed simplices of maximum volume. Beitr Algebra Geom 52, 389–394 (2011). https://doi.org/10.1007/s13366-011-0026-x
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DOI: https://doi.org/10.1007/s13366-011-0026-x