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Historical Overview of the Kepler Conjecture
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  • Published: 27 February 2006

Historical Overview of the Kepler Conjecture

  • Thomas C. Hales1 

Discrete & Computational Geometry volume 36, pages 5–20 (2006)Cite this article

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Abstract

This paper is the first 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. After some preliminary comments about the face-centered cubic and hexagonal close packings, the history of the Kepler problem is described, including a discussion of various published bounds on the density of sphere packings. There is also a general historical discussion of various proof strategies that have been tried with this problem.

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Authors and Affiliations

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

    Thomas C. Hales

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  1. Thomas C. Hales
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Correspondence to Thomas C. Hales.

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Cite this article

Hales, T. Historical Overview of the Kepler Conjecture. Discrete Comput Geom 36, 5–20 (2006). https://doi.org/10.1007/s00454-005-1210-2

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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/s00454-005-1210-2

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Keywords

  • Computational Mathematic
  • Close Packing
  • Historical Overview
  • Sphere Packing
  • Kepler Problem
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