arXiv Analytics

Sign in

arXiv:math/9811072 [math.MG]AbstractReferencesReviewsResources

A formulation of the Kepler conjecture

Samuel P. Ferguson, Thomas C. Hales

Published 1998-11-11, updated 2002-05-20Version 2

This is the second 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 $\pi/\sqrt{18}\approx 0.74048...$. 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 defines a local formulation of the conjecture which is used in the proof.

Comments: 23 pages. Second in a series beginning with math.MG/9811071
Categories: math.MG
Related articles: Most relevant | Search more
arXiv:math/9811071 [math.MG] (Published 1998-11-11, updated 2002-05-20)
An overview of the Kepler conjecture
arXiv:math/9811078 [math.MG] (Published 1998-11-11, updated 2002-06-05)
The Kepler conjecture
arXiv:math/0008151 [math.MG] (Published 2000-08-18)
Bounds for Local Density of Sphere Packings and the Kepler Conjecture

Links

Toolbox