Covering a plane convex body by its negative homothets
type: Item
instance of: scholarly article
title: Covering a plane convex body by its negative homothets
zbMATH Open document ID: 1168.52014
published in: Journal of Geometry
publication date: 2009-06-08T00:00:00Z
review text: The author proves specific results about covering a planar convex body by negative homothets of itself. Namely, let \(\lambda_k\) denote the smallest positive number such that every planar convex body can be covered by \(k\) homothetic copies of itself with homothety ratio \(-\lambda_k\). Confirming a conjecture of Januszewski and Lassak, it is shown that \(\lambda_7=\frac {10}{17}\). Also an estimate on \(\lambda_6\) is given, and the following conjecture is posed: Every planar convex body \(C\) can be covered by five translates of \(-\frac 57C\).
Mathematics Subject Classification ID: 52C15
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 5562639
zbMATH Keywords: covering
zbMATH Keywords: convex body
zbMATH Keywords: homothety
zbMATH Keywords: negative ratio
author: Zsolt Lángi
reviewed by: Horst Martini
MaRDI profile type: Publication
full work available at URL: s00022-008-2076-2
OpenAlex ID: W2024580388
DOI: 10.1007/S00022-008-2076-2
description: scientific article; zbMATH DE number 5562639