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Discrete & Computational Geometry

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

A Formulation of the Kepler Conjecture

  • Thomas C. Hales
  • Samuel P. Ferguson
Article

Abstract

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.

Keywords

Continuous Function Computational Mathematic Topological Space Level Structure Compact Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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