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.
KeywordsEquilateral Triangle Integral Curve Space Curve Continuous Curvature Convex Polyhedron
Unable to display preview. Download preview PDF.