Compact packings in the Euclidean space
type: Item
instance of: scholarly article
title: Compact packings in the Euclidean space
zbMATH Open document ID: 0619.52010
author: Károly Bezdek
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138378
review text: A packing of convex bodies in \({\mathbb{E}}^ n\) is said to be compact if any continuous curve which connects an arbitrary body of the packing with a point sufficiently distant from the body, intersects at least one body of the packing touching the body under consideration. L. Fejes Tóth (oral communication) proved that the lower density of a compact packing of homothetic centrally symmetric convex discs with ratios of diameters bounded is at least 3/4. If the central symmetry is dropped then the lower density is at least 1/2 as shown by A. Bezdek, the author and K. Böröczky [Stud. Sci. Math. Hung., to appear]. The author shows that the density of a compact lattice packing of a centrally symmetric convex body in \({\mathbb{E}}^ n\) is greater than \(2^{1/(n-1)}/(2^{1/(n-1)}+1).\)
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 4005053
zbMATH Keywords: chess-board
zbMATH Keywords: density
zbMATH Keywords: compact lattice packing
zbMATH Keywords: centrally symmetric convex body
reviewed by: Peter M. Gruber
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4005053