Placing and moving spheres in the gaps of a cylinder packing
type: Item
instance of: scholarly article
title: Placing and moving spheres in the gaps of a cylinder packing
zbMATH Open document ID: 0746.52024
published in: Elemente der Mathematik
publication date: 1992-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/141501
review text: The closeness of a packing is defined as the reciprocal of the supremum of the radius of a ball contained in the complement of the packing of \(\mathbb{R}^ 3\) with infinite circular cylinders of radius 1 equals \(\rho^{-1}=3+2\sqrt 3\), and, up to an isometry, the packing of maximum closeness is unique. The authors prove: If in a packing of \(\mathbb{R}^ 3\) no two cylinders are parallel, then, for any two balls of radius \(\rho\) non-overlapping with any of the cylinders, each of the balls can move between the cylinders to assume the other ball's place, without overlapping with any of the cylinders during the motion. This theorem can be strengthened concerning the position of the cylinders (Remark 1); it can also be generalized to \(n\) dimensions (Remark 2).
reviewed by: Johannes Böhm
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 51M05
zbMATH DE Number: 24702
zbMATH Keywords: packings in 3 dimensions
zbMATH Keywords: cylinder packings
zbMATH Keywords: Euclidean geometry
author: A. Bezdek
author: Włodzimierz Kuperberg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 24702