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A Formulation of the Kepler Conjecture
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  • Published: 27 February 2006

A Formulation of the Kepler Conjecture

  • Thomas C. Hales1 &
  • Samuel P. Ferguson2 

Discrete & Computational Geometry volume 36, pages 21–69 (2006)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15217, USA

    Thomas C. Hales

  2. 5960 Millrace Court B-303, Columbia, MD 21045, USA

    Samuel P. Ferguson

Authors
  1. Thomas C. Hales
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  2. Samuel P. Ferguson
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Correspondence to Thomas C. Hales or Samuel P. Ferguson.

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Cite this article

Hales, T., Ferguson, S. A Formulation of the Kepler Conjecture. Discrete Comput Geom 36, 21–69 (2006). https://doi.org/10.1007/s00454-005-1211-1

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  • Received: 11 November 1998

  • Revised: 25 July 2005

  • Published: 27 February 2006

  • Issue Date: July 2006

  • DOI: https://doi.org/10.1007/s00454-005-1211-1

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Keywords

  • Continuous Function
  • Computational Mathematic
  • Topological Space
  • Level Structure
  • Compact Space
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