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Linear Programs for the Kepler Conjecture

(Extended Abstract)

  • Conference paper
Mathematical Software – ICMS 2010 (ICMS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6327))

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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.

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References

  1. GLPK (GNU Linear Programming Kit), http://www.gnu.org/software/glpk/

  2. Fourer, R., Gay, D.M., Kernighan, B.W.: The AMPL book. Brooks/Cole, Monterey (2002)

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  3. Hales, T., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R.: A revision of the proof of the Kepler Conjecture. In: DCG (2009)

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  4. Hales, T.C.: Computer resources for the Kepler conjecture (2003), http://www.math.princeton.edu/~annals/KeplerConjecture/ (2005 snapshot)

  5. Hales, T.C.: The Flyspeck Project (2010), http://code.google.com/p/flyspeck

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    Article  MathSciNet  Google Scholar 

  7. 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 .

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Author information

Authors and Affiliations

  1. University of Pittsburgh,  

    Thomas C. Hales

Authors
  1. Thomas C. Hales
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Editor information

Editors and Affiliations

  1. Institute for Operations Research and Institute of Theoretical Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Komei Fukuda

  2. LIX, CNRS, École polytechnique, 91128, Palaiseau cedex, France

    Joris van der Hoeven

  3. Fachbereich Mathematik, TU Darmstadt, 64289, Darmstadt, Germany

    Michael Joswig

  4. Department of Mathematics, Kobe University, 657-8501, Rokko, Kobe, Japan

    Nobuki Takayama

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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

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  • 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)

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