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Historical Overview of the Kepler Conjecture

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The Kepler Conjecture

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.

Received November 11, 1998, and in revised form September 12, 2003, and July 25, 2005. Online publication February 27, 2006.

The original version of this chapter was revised. An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-1-4614-1129-1_12

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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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  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Jeffrey C. Lagarias

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Hales, T.C. (2011). Historical Overview of the Kepler Conjecture. In: Lagarias, J.C. (eds) The Kepler Conjecture. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1129-1_3

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