Sphere packings V
Metric Geometry
2007-05-23 v1
Abstract
The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program [outlined in math.MG/9811073], a proof that the local density of a certain combinatorial arrangement, the pentahedral prism, is less than that of the face-centered cubic lattice packing. We prove various relations on the local density using computer-based interval arithmetic methods. Together, these relations imply the local density bound.
Cite
@article{arxiv.math/9811077,
title = {Sphere packings V},
author = {Samuel P. Ferguson},
journal= {arXiv preprint arXiv:math/9811077},
year = {2007}
}
Comments
54 pages. Seventh in a series beginning with math.MG/9811071. The author's home page is http://www.math.lsa.umich.edu/~samf/