On the packing of fourteen congruent spheres in a cube
type: Item
instance of: scholarly article
title: On the packing of fourteen congruent spheres in a cube
zbMATH Open document ID: 1228.52012
author: Antal Joós
published in: Geometriae Dedicata
publication date: 2009-06-30T00:00:00Z
review text: The classical problem of finding the configuration of \(n\) points in a unit cube of the 3-dimensional Euclidean space for which the minimum mutual distance is maximal was determined by Schaer, for \(n\leq 10\). In [Math. Mag. 44, 199--208 (1971; Zbl 0228.52004)], \textit{M. Goldberg} has given up to \(n=27\) configurations suspected to be the optimal arrangements. In this paper, the author proves that the maximum of the minimum distance of \(14\) points in the 3-dimensional unit cube is \(\frac{\sqrt 2}{2}\), and at the same time Goldberg's conjecture is proved for \(n=14\).
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 11H31
zbMATH DE Number: 5571620
zbMATH Keywords: packing by equal balls
zbMATH Keywords: finite packing
zbMATH Keywords: dense packings of equal balls in a cube
reviewed by: Jenö Szirmai
MaRDI profile type: Publication
full work available at URL: s10711-008-9308-3
OpenAlex ID: W2073931801
cites work: Q4654164
cites work: Improving dense packings of equal disks in a square
cites work: Research Problems in Discrete Geometry
cites work: Q4530413
cites work: Q3363847
cites work: Dense packings of equal spheres in a cube
cites work: The Packing of Equal Circles in a Square
cites work: On the Densest Packing of Equal Spheres in a Cube
cites work: Die dichteste Packung von 36 Kreisen in einem Quadrat. (On the denest packing of 36 circles in a square)
cites work: Patterns and structures in disk packings
cites work: Optimal packing of 28 equal circles in a unit square -- the first reliable solution
cites work: New results in the packing of equal circles in a square
cites work: Some progress in the packing of equal circles in a square
cites work: Packing up to 50 equal circles in a square
cites work: More optimal packings of equal circles in a square
cites work: Q3139116
cites work: On the Densest Packing of Spheres in a Cube
cites work: The Densest Packing of Five Spheres in a Cube
cites work: The Densest Packing of Six Spheres in a Cube
cites work: The Densest Packing of 9 Circles in a Square
cites work: On the Packing of Ten Equal Circles in a Square
cites work: Q4328202
cites work: On a Geometric Extremum Problem
cites work: Kreispackung in Quadraten
cites work: A better packing of ten equal circles in a square
cites work: Die dichteste Packung von 14 Kreisen in einem Quadrat. (On the densest packing of fourteen circles in a square)
cites work: Q3781682
DOI: 10.1007/S10711-008-9308-3
description: scientific article; zbMATH DE number 5571620