A formulation of the Kepler conjecture
Samuel P. Ferguson, Thomas C. Hales
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/18≈ 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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