Skip to main content

Equidecomposable Quadratic Regions

  • Conference paper
  • 456 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 4869)

Abstract

This article describes an algorithm that decides whether a region in three dimensions, described by quadratic constraints, is equidecomposable with a collection of primitive regions. When a decomposition exists, the algorithm finds the volume of the given region. Applications to the ‘Flyspeck’ project are discussed.

Keywords

  • Irreducible Component
  • Boundary Curve
  • Great Circle
  • Tangent Plane
  • Rigid Motion

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 research has been supported by NSF grant 0503447.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basu, S., Pollack, R., Roy, M.-F.: Algorithms in real algebraic geometry. In: Algorithms and Computation in Mathematics, Second edition, vol. 10, Springer, Berlin (2006)

    Google Scholar 

  2. Berberich, E.: Exact Arrangements of Quadric Intersection Curves, Master’s thesis, Saarbrücken (2004)

    Google Scholar 

  3. Ferguson, S., Hales, T.: The Kepler Conjecture. Disc. and Comp. Geom. 36(1), 1–269 (2006)

    CrossRef  MathSciNet  Google Scholar 

  4. Hales, T.: The Flyspeck Fact Sheet, revised 2007 (2003), http://www.math.pitt.edu/~thales/

  5. Higbee, F.: The Essentials of Descriptive Geometry. Second edition, John Wiley and Sons, New York (1917)

    MATH  Google Scholar 

  6. Laczkovich, M.: Equidecomposability and discrepancy; a solution of Tarski’s circle-squaring problem. J. Reine Angew. Math. 404, 77–117 (1990)

    MATH  MathSciNet  Google Scholar 

  7. Mishra, B.: Computational Real Algebraic Geometry. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, pp. 743–764. CRC Press, Boca Raton FL (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hales, T.C. (2007). Equidecomposable Quadratic Regions . In: Botana, F., Recio, T. (eds) Automated Deduction in Geometry. ADG 2006. Lecture Notes in Computer Science(), vol 4869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77356-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77356-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77355-9

  • Online ISBN: 978-3-540-77356-6

  • eBook Packages: Computer ScienceComputer Science (R0)