We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with...
Erd˝os, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least n−1 2 , which is...
We analyze the minimum and maximum number of empty pseudo-triangles defined by any planar point set. We consider the cases where the three convex vertices are fixed and where th...
Given n points in the plane, we study three optimization problems of computing an empty pseudo-triangle: we consider minimizing the perimeter, maximizing the area, and minimizing ...