Covering a convex body by its negative homothetic copies

Janusz Januszewski and Marek Lassak

Vol. 197 (2001), No. 1, 43–51

DOI: 10.2140/pjm.2001.197.43

Abstract

We estimate the number and ratio of negative homothetic copies of a d-dimensional convex body C sufficient for the covering of C. If the number of those copies is not very large, then our estimates are better than recent estimates of Rogers and Zong. Particular attention is paid to the 2-dimensional case. It is proved that every planar convex body can be covered by two copies of ratio − (this ratio cannot be lessened if C is a triangle).

Milestones

Received: 1 March 1999

Published: 1 January 2001