The Kepler conjecture

Details The Kepler conjecture The Kepler conjecture

1998-11-11

arxiv.org/abs/math/9811078v2

Mathematics

Metric Geometry

62 pages. Eighth and last in a series beginning with math.MG/9811071. Includes an index of terminology and notation for the en

Scientific paper

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 $8 \pt$.

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