The Kepler Conjecture

pp 83-133


A Formulation of the Kepler Conjecture

  • Thomas C. HalesAffiliated withDepartment of Mathematics, University of Pittsburgh Email author 
  • , Samuel P. FergusonAffiliated with

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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.