Packings of unequal circles in a convex set
type: Item
instance of: scholarly article
title: Packings of unequal circles in a convex set
zbMATH Open document ID: 1010.52015
published in: Discrete \& Computational Geometry
publication date: 2002-08-20T00:00:00Z
review text: The authors prove the following result. Suppose that \(T\) is a convex set in the Euclidean plane, and let \(K_1,\dots, K_n\) be \(n\geq 2\) circles packed in \(T\). Suppose further that \(K_i\) has radius \(r_i\), and that \[ {\min r_i\over\max r_i}\geq a_0, \] with \(a_0\) defined by \[ a^2_0:= {a(6)- a(7)\over a(5)- a(6)}, \] where \(a(p):= p\tan (\pi/p)\) is the area of the regular \(p\)-gon circumscribed to the unit circle. Then the density of the packing is at most \(\pi/\sqrt{12}\), namely, that of the closest packing of circles in the plane. They also obtain better bounds for \(2\) and \(3\) circles, that for the former being exact.
Mathematics Subject Classification ID: 52C26
zbMATH DE Number: 1784799
zbMATH Keywords: circle packing
zbMATH Keywords: convex set
zbMATH Keywords: density
author: G. Blind
author: Roswitha Blind
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: s00454-001-0094-z
OpenAlex ID: W2047412641
DOI: 10.1007/S00454-001-0094-Z
description: scientific article; zbMATH DE number 1784799