The Tammes Problem for N=14

被引：30

作者：

Musin, Oleg R. ^{[1
]}

Tarasov, Alexey S. ^{[2
]}

机构：

[1] Univ Texas Brownsville, Brownsville, TX 78520 USA

[2] IITP RAS, Moscow, Russia

来源：

EXPERIMENTAL MATHEMATICS | 2015年 / 24卷 / 04期

基金：

美国国家科学基金会;

关键词：

Tammes problem; sphere packing; irreducible contact graph; 13; SPHERES; DIMENSIONS; BOUNDS; NUMBER; PROOF;

D O I：

10.1080/10586458.2015.1022842

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Tammes problem is to find the arrangement of N points on a unit sphere which maximizes the minimum distance between any two points. This problem is presently solved for several values of N, namely for N = 3, 4, 6, 12 by L. Fejes Toth (1943); for N = 5, 7, 8, 9 by Schutte and van der Waerden (1951); for N = 10, 11 by Danzer (1963); and for N = 24 by Robinson (1961). Recently, we solved the Tammes problem for N = 13. The optimal configuration of 14 points was conjectured more than 60 years ago. In this article, we give a solution for this long-standing open problem in geometry. Our computer-assisted proof relies on an enumeration of the irreducible contact graphs.

引用

页码：460 / 468

页数：9

共 28 条

[1]

[Anonymous], RYUKYU MATH J

[2]

[Anonymous], 2014, Proofs from The Book

[3]

[Anonymous], 2004, Notices Amer. Math. Soc.

[4] The thirteen spheres: A new proof [J].