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A formulation of the Kepler conjecture

Samuel P. Ferguson·Thomas C. Hales
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Abstract

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 $π/\sqrt{18}\approx 0.74048...$. 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.

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Samuel P. Ferguson, Thomas C. Hales. 2002-05-20. A formulation of the Kepler conjecture. https://arxiv.org/abs/math/9811072

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