Approximation of convex bodies by inscribed simplices of maximum volume

Open Access
Original Paper

Abstract

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space En 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 En 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.

Keywords

Approximation Banach–Mazur distance Convex body Double-cone Simplex Volume 

Mathematics Subject Classification (2000)

52A21 52A10 46B20 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and PhysicsUniversity of TechnologyBydgoszczPoland

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