Discrete & Computational Geometry

, Volume 36, Issue 1, pp 21–69 | Cite as

A Formulation of the Kepler Conjecture

  • Thomas C. HalesEmail author
  • Samuel P. FergusonEmail author


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.


Continuous Function Computational Mathematic Topological Space Level Structure Compact Space 
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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

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