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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: 103 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.

Date Subject Author
7/29/08 Steve Gray
7/29/08 Lee Rudolph
8/5/08 Steve Gray

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