Discrete & Computational Geometry

, Volume 36, Issue 1, pp 21–69

A Formulation of the Kepler Conjecture


DOI: 10.1007/s00454-005-1211-1

Cite this article as:
Hales, T. & Ferguson, S. Discrete Comput Geom (2006) 36: 21. doi:10.1007/s00454-005-1211-1


This paper is the second in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. The top level structure of the proof is described. A compact topological space is described. Each point of this space can be described as a finite cluster of balls with additional combinatorial markings. A continuous function on this compact space is defined. It is proved that the Kepler conjecture will follow if the value of this function is never greater than a given explicit constant.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15217USA
  2. 2.5960 Millrace Court B-303, Columbia, MD 21045USA