Packing 16, 17 or 18 circles in an equilateral triangle
type: Item
instance of: scholarly article
title: Packing 16, 17 or 18 circles in an equilateral triangle
zbMATH Open document ID: 0836.52006
DOI: 10.1016/0012-365X(95)90139-C
author: J. B. M. Melissen
author: Peter Cornelis Schuur
published in: Discrete Mathematics
publication date: 1995-12-03T00:00:00Z
review text: What is the smallest circle, or square, or equilateral triangle etc., that can contain \(n\) nonoverlapping unit circles? After giving a survey on results related to this problem, the authors consider the case of equilateral triangles for the special values \(n\in \{16, 17, 18\}\), filling a gap in the literature. They present efficient packings for these cases. Clearly, the problem of finding the largest common radius \(r_n\) of \(n\) congruent circles inside a unilateral triangle \(T\) is equivalent to maximizing the minimum pairwise distance \(t_n\) of \(n\) points in \(T\). By the homothety between \(T\) and the smallest equilateral triangle containing their centers, the relation \[ t_n= {{2r_n} \over {1-2 \sqrt {3r_n}}} \] between \(r_n\) and \(t_n\) is obtained. For the latter problem, two numerical methods generating near-optimal solutions are described.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52C15
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 810280
zbMATH Keywords: circle packings
zbMATH Keywords: separation problem
zbMATH Keywords: equi-distant graphs
Wikidata QID: Q56169159
MaRDI profile type: Publication
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DBLP publication ID: journals/dm/MelissenS95
description: scientific article; zbMATH DE number 810280