An Improved Bound on the Number of Unit Area Triangles

Abstract

We show that the number of unit-area triangles determined by a set of $n$ points in the plane is $O(n^{9/4+\epsilon })$, for any $\epsilon >0$, improving the recent bound $O(n^{44/19})$ of Dumitrescu et al.

12 pages, 2 figures, appeared in the 25th Annual Symposium on Computational Geometry (2009), submitted to "Discrete and Computational Geometry"

References in corpus (1)

• Extremal problems on triangle areas in two and three dimensions