Covering a square by equal circles
type: Item
instance of: scholarly article
title: Covering a square by equal circles
zbMATH Open document ID: 0847.52018
author: Tibor Tarnai
author: Zsolt Gáspár
published in: Elemente der Mathematik
publication date: 1996-03-04T00:00:00Z
full work available at URL: https://eudml.org/doc/141584
review text: Results for the finite packing problem of \(n\) equal circles in the unit square \(S\) are well known for many numbers \(n\). Corresponding results for the dual finite covering problem seem to be unknown: What is the smallest radius \(r_n\) of \(n\) equal circles which can cover \(S\) and how must \(S\) be covered? The authors associate with a covering of \(S\) a bipartite graph which is interpreted as a network of straight bars. With an interesting physical ``cooling technique'' as developed by the authors [Math. Proc. Camb. Philos. Soc. 110, No. 1, 71-89 (1991; Zbl 0736.52009)] they have discovered locally optimal coverings for all \(n\leq 10\). The results for \(r_n\) and the conjectured minimum density are collected in a table without details of the calculations.
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 850642
zbMATH Keywords: covering by circles
zbMATH Keywords: finite covering
zbMATH Keywords: minimum density
reviewed by: Eike Hertel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 850642