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arXiv:math/9811078 [math.MG]AbstractReferencesReviewsResources

The Kepler conjecture

Thomas C. Hales

Published 1998-11-11, updated 2002-06-05Version 2

This is the eighth and final paper in a series 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 completes the fourth step of the program outlined in math.MG/9811073: A proof that if some standard region has more than four sides, then the star scores less than $8 \pt$.

Comments: 62 pages. Eighth and last in a series beginning with math.MG/9811071. Includes an index of terminology and notation for the entire series. The source package of the first version includes the source code of the software used in the proof. The second version has been completely rewritten
Categories: math.MG
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arXiv:math/9811071 [math.MG] (Published 1998-11-11, updated 2002-05-20)
An overview of the Kepler conjecture
arXiv:math/9811072 [math.MG] (Published 1998-11-11, updated 2002-05-20)
A formulation of the Kepler conjecture
arXiv:math/0008151 [math.MG] (Published 2000-08-18)
Bounds for Local Density of Sphere Packings and the Kepler Conjecture

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