A formulation of the Kepler conjecture

Details A formulation of the Kepler conjecture A formulation of the Kepler conjecture

1998-11-11

arxiv.org/abs/math/9811072v2

Mathematics

Metric Geometry

23 pages. Second in a series beginning with math.MG/9811071

Scientific paper

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.

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