Skip to main content

Computational Discrete Geometry

  • Conference paper
  • 1640 Accesses

Part of the Lecture Notes in Computer Science book series (LNTCS,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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Aristotle, On the heaven, translated by J.L. Stocks, 350BC, http://classics.mit.edu/Aristotle/heavens.html

  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. Chen, B., Engel, M., Glotzer, S.C.: Dense crystalline dimer packings of regular tetrahedra (2010), http://arxiv.org/abs/1001.0586

  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

    CrossRef  MATH  MathSciNet  Google Scholar 

  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. Hales, T.C., Ferguson, S.P.: Kepler conjecture. Discrete and Computational Geometry 36(1), 1–269 (2006)

    CrossRef  MathSciNet  Google Scholar 

  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. Lagrange, J.L.: Recherches d’arithmétique. Mem. Acad. Roy. Sc. Bell Lettres Berlin 3, 693–758 (1773); Volume and pages refer to Œuvres

    Google Scholar 

  9. Musin, O.R., Tarasov, A.S.: The strong thirteen spheres problem (February 2010) (preprint), http://arxiv.org/abs/1002.1439

  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

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hales, T.C. (2010). Computational Discrete Geometry. 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_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15582-6_1

  • 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)