On the density of dual circle coverings
type: Item
instance of: scholarly article
title: On the density of dual circle coverings
zbMATH Open document ID: 0699.52003
DOI: 10.1007/BF00183086
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: Let C be a family of distinct unit circles in the Euclidean plane. The dual of the family C is the collection \(C^*\) of all unit circles which are centered at points belonging to the boundary of at least two members of C. If C is a covering of the plane, then so is \(C^*\). Let \(d^-(C)\) denote the lower density of the family C. The main theorem states that \(d^-(C)\leq d^-(C^*)\) for any covering C by unit circles. \textit{K. Bezdek} and \textit{R. Connelly} [Ann. Univ. Sci. Budapest Rolando Eötvös, Sect. Math. 31, 115-127 (1988; Zbl 0683.52014)] have proved this inequality for such coverings C which contain no pair of tangent circles.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 4146977
zbMATH Keywords: covering by circles
zbMATH Keywords: density
author: A. Bezdek
reviewed by: August Florian
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00183086
OpenAlex ID: W2027015571
description: scientific article; zbMATH DE number 4146977