Sphere packings III
Metric Geometry
2007-05-23 v2
Abstract
This is the fifth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than . This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper carries out the third step of the program outlined in math.MG/9811073: A proof that if all of the standard regions are triangles or quadrilaterals, then the total score is less than (excluding the case of pentagonal prisms).
Cite
@article{arxiv.math/9811075,
title = {Sphere packings III},
author = {Thomas C. Hales},
journal= {arXiv preprint arXiv:math/9811075},
year = {2007}
}
Comments
22 pages. Fifth in a series beginning with math.MG/9811071