Year: 1998
Type: preprint
Abstract: 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 $π/\sqrt{18}\approx 0.74048...$. 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 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 $8 \pt$.
Source: arXiv (Cornell University)
Author: Hales, Thomas C.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1607529908