Discrete & Computational Geometry

, Volume 9, Issue 3, pp 257–266 | Cite as

An equipartition of planar sets

  • Leonard J. Schulman


We describe the “cobweb” partition scheme and show that it can split any planar set into eight regions of equal area.


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  1. 1.
    M. Adams and V. Guillemin.Measure Theory and Probability, Wadsworth, Monterey, CA, 1986.MATHGoogle Scholar
  2. 2.
    B. Aronov, P. Erdös, W. Goddard, D. J. Kleitman, M. Klugerman, J. Pach, and L. J. Schulman. Crossing families. InProc. Seventh ACM Symp. on Computational Geometry, pp. 351–356, 1991.Google Scholar
  3. 3.
    R. C. Buck and E. F. Buck. Equartition of convex sets.Math. Mag., 22:195–198, 1987.MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Courant and H. Robbins.What is Mathematics, pp. 317–319. Oxford University Press, Oxford, 1941.Google Scholar
  5. 5.
    H. Edelsbrunner and F. Huber. Dissecting Sets of Points in Two and Three Dimensions. Technical Report F138, Technische Universitat Graz, 1984.Google Scholar
  6. 6.
    J. Matoušek. Efficient partition trees. InProc. Seventh ACM Symp. on Computational Geometry, pp. 1–9, 1991.Google Scholar
  7. 7.
    J. R. Munkres.Topology: A First Course. Prentice-Hall, Englewood Cliffs, NJ, 1975.MATHGoogle Scholar
  8. 8.
    W. Rudin.Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York, 1976.MATHGoogle Scholar
  9. 9.
    R. M. Switzer.Algebraic Topology—Homotopy and Homology. Springer-Verlag, Berlin, 1975.CrossRefMATHGoogle Scholar
  10. 10.
    D. E. Willard. Polygon retrieval.SIAM J. Comput., 11(1):149–165, February 1982.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    A. C. Yao and F. F. Yao. A general approach tod-dimensional geometric queries. InProc. 17th Symp. on Theory of Computing, pp. 163–169, 1985.Google Scholar
  12. 12.
    F. F. Yao. Computational geometry. In J. van Leeuwen, ed.,Handbook of Theoretical Computer Science, Volume A, Chapter 7. Elsevier, Amsterdam, 1990.Google Scholar
  13. 13.
    F. F. Yao, D. P. Dobkin, H. Edelsbrunner, and M. S. Paterson. Partitioning space for range queries.SIAM J. Comput., 18(2):371–384, April 1989.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Leonard J. Schulman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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