1998/11/11 by Thomas C. Hales, Hales, Thomas C. · 1 citation
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.math/9811071
16 pages. First in a series
arxiv created 2002/05/20 · arxiv updated 2009/11/30
This is the first 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 has a historical overview and a synopsis of the rest of the series. The other papers in the series are math.MG/9811072, math.MG/9811073, math.MG/9811074, math.MG/9811075, math.MG/9811076, math.MG/9811077, and math.MG/9811078.