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Interesting problems in discrete geometry
Posted:
Jul 29, 2008 5:16 PM


1. Given a convex point set in R3 plus one point P inside its convex hull, show that one can always find a tetrahedron T whose vertices belong to the point set, that encloses the interior point.
2. Show that any central or parallel projection onto R2 of T and P is a quadrilateral T' enclosing P.
3. Therefore any point set having at least one convex projection is convex.
These seem almost obvious but that's not the same as proved.



