The Strong Thirteen Spheres Problem

Authors

Oleg R. Musin, The University of Texas Rio Grande Valley
Alexey S. Tarasov

Document Type

Article

Publication Date

7-2012

Abstract

The thirteen spheres problem asks if 13 equal-size non-overlapping spheres in three dimensions can simultaneously touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schütte and van der Waerden only in 1953.

A natural extension of this problem is the strong thirteen-sphere problem (or the Tammes problem for 13 points), which calls for finding the maximum radius of and an arrangement for 13 equal-size non-overlapping spheres touching the unit sphere. In this paper, we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on an enumeration of irreducible graphs.

Comments

Copyright © 2012, Springer Science Business Media, LLC

https://rdcu.be/c50Qw

Recommended Citation

Musin, O.R., Tarasov, A.S. The Strong Thirteen Spheres Problem. Discrete Comput Geom 48, 128–141 (2012). https://doi.org/10.1007/s00454-011-9392-2

Publication Title

Discrete Comput Geom

DOI

10.1007/s00454-011-9392-2