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Computational Discrete Geometry

  • Thomas C. Hales
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

Abstract

In recent years, computers have been used regularly to solve major problems in discrete geometry. The talk at ICMS 2010 will give a survey of the computational methods. The extended abstract that is provided below mentions a few of the problems that will be discussed.

Keywords

Planar Graph Circle Packing Assisted Proof Lattice Packing Regular Tetrahedron 
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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References

  1. 1.
    Aristotle, On the heaven, translated by J.L. Stocks, 350BC, http://classics.mit.edu/Aristotle/heavens.html
  2. 2.
    Brinkmann, G., McKay, B.D.: Fast generation of planar graphs, expanded edition (2007), http://cs.anu.edu.au/~bdm/papers/plantri-full.pdf
  3. 3.
    Chen, B., Engel, M., Glotzer, S.C.: Dense crystalline dimer packings of regular tetrahedra (2010), http://arxiv.org/abs/1001.0586
  4. 4.
    Cohn, H., Kumar, A.: The densest lattice in twenty-four dimensions. Electronic Research Annoucements of the American Mathematical Society 10, 58–67 (2004), math.MG/0408174 zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gauss, C.F.: Untersuchungen über die Eigenscahften der positiven ternären quadratischen Formen von Ludwig August Seber. Göttingische gelehrte Anzeigen (1831); Also published in J. reine angew. Math. 20, 312–320 (1840), Werke 2. Königliche Gesellschaft der Wissenschaften, Göttingen, 188–196 (1876)Google Scholar
  6. 6.
    Hales, T.C., Ferguson, S.P.: Kepler conjecture. Discrete and Computational Geometry 36(1), 1–269 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hilbert, D.: Mathematische probleme. Archiv Math. Physik 1, 44–63 (1901); Also in Proc. Sym. Pure Math. 28, 1–34 (1976) Google Scholar
  8. 8.
    Lagrange, J.L.: Recherches d’arithmétique. Mem. Acad. Roy. Sc. Bell Lettres Berlin 3, 693–758 (1773); Volume and pages refer to ŒuvresGoogle Scholar
  9. 9.
    Musin, O.R., Tarasov, A.S.: The strong thirteen spheres problem (February 2010) (preprint), http://arxiv.org/abs/1002.1439
  10. 10.
    Torquato, S., Jiao, Y.: Exact constructions of a family of dense periodic packings of tetrahedra. Physical Review E 81, 041310–1–11 (2010), http://cherrypit.princeton.edu/papers.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Thomas C. Hales
    • 1
  1. 1.University of Pittsburgh 

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