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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Anonymous, What every computer scientist should know about floatingpoint arithmetic, http://docs.sun.com/htmlcoll/coll.648.2/iso-8859-1/NUMCOMPGD/ncggoldberg.html/htmlcoll/coll.648.2/iso-8859-1/NUMCOMPGD/ncggoldberg.html
S. Basu, R. Pollack, and M.-F. Roy, On the combinatorial and algebraic complexity of Quantifier Elimination, In Procedings of the Foundations of Computer Science, pp. 632–641, 1994.
Goetz Alefeld and Juergen Herzberger, Introduction to Interval Computations, Academic Press, N.Y., 1983.
Krzysztof Czarnecki and Ulrich Eisenecker, Generative Programming: Methods, Tools, and Applications, Addison-Wesley, 2000.
Bob F. Caviness (Editor), J. R. Johnson (Editor), Quantifier Elimination and Cylindrical Algebraic Decomposition (Texts and Monographs in Symbolic Computation), Springer-Verlag, 1998.
S. Ferguson and T. Hales, A formulation of the Kepler conjecture, preprint, 1998.
T. Hales, Sphere Packings I, 0000 Disc. Comp. Geom, 1997, 17:1–51.
T. Hales, An overview of the Kepler conjecture, preprint, 1998.
T. Hales, Sphere Packings III, preprint, 1998.
Reiner Horst, P. M. Pardalos, and Nguyen V. Thoai, Introduction to Global Optimization - Second Edition (Nonconvex Optimization and its Applications, Volume 48), Kluwer, 2000.
Andrew Hunt, David Thomas, and Ward Cunningham Pragmatic Programmer: From Journeyman to Master, Addison-Wesley, 1999.
R. Baker Kearfott: Rigorous Global Search: Continuous Problems Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.
Bhubaneswar Mishra, Computational Real Algebraic Geometry, Handbook of Discrete and Computational Geometry, CRC Press, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
