An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
type: Item
instance of: scholarly article
title: An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
zbMATH Open document ID: 0941.52016
DOI: 10.1023/A:1005056207406
author: I. Papadoperakis
published in: Geometriae Dedicata
publication date: 2000-07-31T00:00:00Z
review text: Let \(A\) be a convex body in Euclidean space \(\mathbb E^n.\) Let \(H(A)\) be the smallest number of homothetic ``reduced copies'' of \(A\) by which it is possible to cover the whole of \(A.\) The conjecture of Hadwiger is \(H(A) \leqslant 2^n\) [\textit{H.~Hadwiger}, Ungelöste Probleme. 20, Elem. Math. 12, 121 (1957)]. The author proves that \(H(A) \leqslant 16,\) for \(n=3.\)
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 1334360
zbMATH Keywords: convex body
zbMATH Keywords: Euclidean space
zbMATH Keywords: conjecture of Hadwiger
zbMATH Keywords: covering convex body by smaller homothetic copies
zbMATH Keywords: tiling problem
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
full work available at URL: a:1005056207406
OpenAlex ID: W170630596
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description: scientific article; zbMATH DE number 1334360