Geometric Problems

  • George Pólya
  • Gabor Szegö
Part of the Springer Study Edition book series (SSE)

Abstract

If we throw a heavy convex polyhedron with arbitrary interior mass distribution onto a horizontal floor then it will come to rest in a stable position on one of its faces. That is there exists for an arbitrary point P lying in the interior of the convex polyhedron one face F (at least) with the following property: The perpendicular dropped from P onto the plane in which F lies has its foot in the interior of the face F. Give a purely geometrical proof free from mechanical considerations for the existence of the face F.

Keywords

Equilateral Triangle Integral Curve Space Curve Continuous Curvature Convex Polyhedron 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • George Pólya
    • 1
  • Gabor Szegö
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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