The Number of Isosceles Right Triangles Determined by n Points in Convex Position in the Plane

Abstract

Any set of n points in convex position in the plane induces at most 2n congruent copies of a fixed isosceles triangle. Furthermore, at most 2n–4 congruent isosceles right triangles can be induced by a set of n points in convex position, and in strictly convex position at most n congruent isosceles right triangles can be induced.