The Minimum Number of Distinct Areas of Triangles Determined by a Set of n Points in the Plane

We prove a conjecture of Erdos, Purdy, and Straus on the number of distinct areas of triangles determined by a set of n points in the plane. We show that if P is a set of n points in the plane, not all on one line, then P determines at least n-1 2 triangles with pairwise distinct areas. Moreover, one can find such n-1 2 triangles all sharing a common edge.

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Rom Pinchasi
• Keywords: Conjecture, Distinct Areas, SIAMDM 2008, Triangles