Covering a plane convex body with five smaller homothetical copies
type: Item
instance of: scholarly article
title: Covering a plane convex body with five smaller homothetical copies
zbMATH Open document ID: 0619.52003
author: Sławomir Krotoszyński
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138385
review text: A conjecture of Marek Lassak (1986) concerning Hadwiger's covering problem is solved: For a convex body C in the Euclidean plane, let \(h_ k(C)\) be the smallest positive ratio of k homothetical copies of C whose union covers C. Define \(h_ k=\inf \{h_ k(C): C\) is a plane convex body\(\}\). Then \(h_ 5=1/2\). Lassak also formulated the conjecture that \(h_ 6=1/2\), but this is still unsolved.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 4005046
zbMATH Keywords: Hadwiger's covering problem
zbMATH Keywords: convex body
zbMATH Keywords: Euclidean plane
zbMATH Keywords: homothetical copies
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4005046