Translative covering by homothetic copies
type: Item
instance of: scholarly article
title: Translative covering by homothetic copies
zbMATH Open document ID: 0783.52012
DOI: 10.1007/BF01264916
author: Yanyan Li
published in: Geometriae Dedicata
publication date: 1994-03-14T00:00:00Z
review text: The authors prove the following nice theorem using elementary geometry only: For every convex disc \(K\) in the Euclidean plane there are homothetic triangles \(T\) and \(\lambda T\) with \(T\subseteq K\subseteq \lambda T\) and \(\lambda = 3(\sqrt{17}-1)/4\). As a corollary the authors give the sufficient condition \(\sum V(K_ i) \geq 9(9-\sqrt{17})/4\) for the existence of a translative covering of \(K\) with area \(V(K) = 1\) by any sequence \((K_ i)\) of homothetic copies of \(K\).
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 205530
zbMATH Keywords: translative covering
zbMATH Keywords: convex disc
zbMATH Keywords: homothetic copies
reviewed by: Eike Hertel
MaRDI profile type: Publication
cites work: A sufficient condition for the covering of the unit cube by homothetic copies in the \(n\)-dimensional Euclidean space
cites work: Covering and packing properties of bounded sequences of convex sets
cites work: Q3695936
cites work: Approximation of Plane Convex Bodies by Centrally Symmetric Bodies
cites work: Approximation of Convex Bodies by Triangles
cites work: Q4019770
cites work: On packing of squares and cubes
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description: scientific article; zbMATH DE number 205530