Department of
Applied
Mathematics

On the number of unit-area triangles spanned by points in the plane

Orit Raz

Abstract

We show that the number of unit-area triangles determined by a set S of n points in the plane is O(n^{20/9}), improving the earlier bound O(n^{9/4}) of Apfelbaum and Sharir. We also show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles can be \Omega(n^2). This is a joint work with Micha Sharir.