Abstract
The Kepler conjecture asserts that the densest arrangement of congruent balls in Euclidean three-space is the face-centered cubic packing, which is the familiar pyramid arrangement used to stack oranges at the market. The problem was finally solved in 1998 by a long computer proof. The Flyspeck project seeks to give a full formal proof of the Kepler conjecture. This is an extended abstract for a talk in the formal proof session of ICMS-2010, which will describe the linear programming aspects of the Flyspeck project.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
GLPK (GNU Linear Programming Kit), http://www.gnu.org/software/glpk/
Fourer, R., Gay, D.M., Kernighan, B.W.: The AMPL book. Brooks/Cole, Monterey (2002)
Hales, T., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R.: A revision of the proof of the Kepler Conjecture. In: DCG (2009)
Hales, T.C.: Computer resources for the Kepler conjecture (2003), http://www.math.princeton.edu/~annals/KeplerConjecture/ (2005 snapshot)
Hales, T.C.: The Flyspeck Project (2010), http://code.google.com/p/flyspeck
Hales, T.C., Ferguson, S.P.: The Kepler conjecture. Discrete and Computational Geometry 36(1), 1–269 (2006)
Obua, S.: Flyspeck II: The basic linear programs, Ph.D. thesis, Technische Universität München (2008), http://deposit.d-nb.de/cgi-bin/dokserv?idn=992033632&dok_var=d1&dok_ext=pdf&filename=992033632.pdf , http://mediatum2.ub.tum.de/doc/645669/645669.pdf .
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hales, T.C. (2010). Linear Programs for the Kepler Conjecture. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-15582-6_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
Online ISBN: 978-3-642-15582-6
eBook Packages: Computer ScienceComputer Science (R0)