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Some Algorithms Arising in the Proof of the Kepler Conjecture

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Part of the Algorithms and Combinatorics book series (AC,volume 25)

Abstract

By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones would have been better suited. This paper gives a series of nonlinear optimization algorithms and shows how a systematic application of these algorithms would bring substantial simplifications to the original proof.

Keywords

  • Dual Problem
  • Voronoi Cell
  • Interval Arithmetic
  • Local Domain
  • Terminal Vertex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Hales, T.C. (2003). Some Algorithms Arising in the Proof of the Kepler Conjecture. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_22

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  • DOI: https://doi.org/10.1007/978-3-642-55566-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62442-1

  • Online ISBN: 978-3-642-55566-4

  • eBook Packages: Springer Book Archive