From:grove@ernie.Berkeley.EDU (Eddie Grove)Newsgroups:sci.mathSubject:Special Triangulations of Convex PolygonsDate:6 Mar 90 20:01:32 GMTReply-To:grove@ernie.Berkeley.EDU.UUCP (Eddie Grove)Organization:University of California, Berkeley

A triangulation of a an n-vertex convex polygon is a partition by n-3 chords into n-2 triangles. No 2 of the chords intersect in the interior of the polygon. I want to know how many different areas are possible. Formally, I want a function t(n) as large as possible (linear would be ideal) satisfying: for all n-vertex convex polygons there exists a triangulation containing at least t(n) triangles of different areas. I have not seen how to create an example in which 3 triangles must have the same area. I would be interested in such an example, if it exists. The polygons I am interested in are special. They lie in planes in R^3, and all of the vertices are lattice points, within the m x m x m cube. The normal directions to the planes can be written with integer coordinates at most m. An answer in terms of m would be helpful, although less satisfying. Eddie Grove Eddie Grove