Open Access
Original Paper

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

, 52:389

Approximation of convex bodies by inscribed simplices of maximum volume

Authors

  • Marek Lassak
    • Institute of Mathematics and PhysicsUniversity of Technology

DOI: 10.1007/s13366-011-0026-x

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.

Keywords

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

Mathematics Subject Classification (2000)

52A21 52A10 46B20

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Copyright information

© The Author(s) 2011