Discrete & Computational Geometry

, Volume 36, Issue 1, pp 5–20 | Cite as

Historical Overview of the Kepler Conjecture

  • Thomas C. HalesEmail author


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.


Computational Mathematic Close Packing Historical Overview Sphere Packing Kepler Problem 
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Copyright information

© Springer 2006

Authors and Affiliations

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

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