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A Formulation of the Kepler Conjecture

In: The Kepler Conjecture

Author

Listed:
  • Thomas C. Hales

    (University of Pittsburgh, Department of Mathematics)

  • Samuel P. Ferguson

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.

Suggested Citation

  • Thomas C. Hales & Samuel P. Ferguson, 2011. "A Formulation of the Kepler Conjecture," Springer Books, in: Jeffrey C. Lagarias (ed.), The Kepler Conjecture, chapter 4, pages 83-133, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-1129-1_4
    DOI: 10.1007/978-1-4614-1129-1_4
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