The strong thirteen spheres problem
Abstract
The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can 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 Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this longstanding open problem in geometry. Our computerassisted proof is based on a enumeration of the socalled irreducible graphs.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1002.1439
 Bibcode:
 2010arXiv1002.1439M
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Combinatorics;
 52C15 (Primary) 05B40 (Secondary)
 EPrint:
 Modified lemma 2, 16 pages, 12 figures. Uploaded program package