Results

**1 - 1**of**1**### The Number of Unit-Area Triangles in the Plane: Theme and Variations *

"... 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 (ii) We show that if S is a convex grid of the form A × B, where A, B are convex sets of n 1/2 real numbers each (i.e. ..."

Abstract
- Add to MetaCart

(Show Context)
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 (ii) We show that if S is a convex grid of the form A × B, where A, B are convex sets of n 1/2 real numbers each (i.e., the sequences of differences of consecutive elements of A and of B are both strictly increasing), then S determines O(n 31/14 ) unit-area triangles.