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.
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© 1989 Springer-Verlag Berlin Heidelberg
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Pólya, G., Szegö, G. (1989). Geometric Problems. In: Problems and Theorems in Analysis II. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61905-2_6
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DOI: https://doi.org/10.1007/978-3-642-61905-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63686-1
Online ISBN: 978-3-642-61905-2
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