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Discrete & Computational Geometry

, Volume 5, Issue 6, pp 529–531 | Cite as

Convex disks can cover their shadow

  • Géza Kós
  • Jenő Törőcsik
Article

Abstract

We give a short proof of the fact that given any two-dimensional convex disk in three-space and an orthogonal projectionC′ ofC on a plane then there is a congruent copy ofC which containsC′.

Keywords

Orthogonal Projection Parallel Line Discrete Comput Geom Convex Compact Computational Geometry 
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.

References

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    V. A. Zalgaller, The imbedding of one figure in another,Ukrainskij Geometriceskij Sbornik,10/71 (1971), 19–20 (in Russian).MathSciNetzbMATHGoogle Scholar
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    J. Pach, Communication at the problem session,Tagung über konvexe Körper, Oberwolfach, 1984.Google Scholar
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    M. D. Kowaljov, Covering a convex figure by its images under dilatation,Ukrainskij Geometriceskij Sbornik,27/84 (1984), 57–68 (in Russian).Google Scholar
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    H. E. Debrunner and P. Mani-Levitska, Can you cover your shadows?,Discrete & Computational Geometry,1 (1986), 45–58.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Géza Kós
    • 1
  • Jenő Törőcsik
    • 1
  1. 1.Department of MathematicsEötrös UniversityBudapestHungary

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