On a problem of G. Fejes Tóth
type: Item
instance of: scholarly article
title: On a problem of G. Fejes Tóth
zbMATH Open document ID: 0799.52013
DOI: 10.1007/BF02830878
author: R. P. Bambah
author: A. C. Woods
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1994-07-04T00:00:00Z
review text: The authors prove the following Theorem: Let \(L \subset E^ 3\) be a lattice and \(B^ 3\) the unit 3-ball. If each straight line meets \(L+B^ 3\), then \(\text{det} L \leq 2 (4/3)^ 3\). In terms of density such an arrangement has a density \(V(B^ 3)/ \text{det} L = 0,8835\dots\) The theorem is a partial solution of the following general problem by G. Fejes Tóth: In \(n\)-space find the thinnest lattice arrangement of closed balls such that every \(k\)-dimensional \((0 \leq k \leq n - 1)\) flat meets one of these balls.
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 562807
zbMATH Keywords: lattice
zbMATH Keywords: unit 3-ball
zbMATH Keywords: density
zbMATH Keywords: thinnest lattice arrangement
zbMATH Keywords: balls
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Q3751649
cites work: Q3207690
description: scientific article; zbMATH DE number 562807