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Topic: Interesting problems in discrete geometry
Replies: 2   Last Post: Aug 5, 2008 4:59 PM

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Steve Gray

Posts: 101
Registered: 7/6/07
Interesting problems in discrete geometry
Posted: Jul 29, 2008 5:16 PM
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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.



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