Triangles of extremal area or perimeter in a finite planar point set.

We show the following two results on a set of n points in the plane, thus answering questions posed by Erdos and Purdy [11]: 1. The maximum number of triangles of maximum area (or of maximum perimeter) in a set of n points in the plane is exactly n . 2. The maximum possible number of triangles of minimum positive area in a set of n points in the plane is Θ(n 2 ) .