We show that the number of unit-area triangles determined by a set of n points in the plane is O(n9/4+ε), for any ε > 0, improving the recent bound O(n44/19) of Dumitrescu et...
The study of extremal problems on triangle areas was initiated in a series of papers by Erdos and Purdy in the early 1970s. In this paper we present new results on such problems, ...
Adrian Dumitrescu, Micha Sharir, Csaba D. Tó...
The n-th Heilbronn number, Hn, is the largest value such that n points can be placed in the unit square in such a way that all possible triangles defined by any three of the point...
The four-triangles longest-edge (4T-LE) partition of a triangle t is obtained by joining the midpoint of the longest edge of t to the opposite vertex and to the midpoints of the t...
Erd˝os, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least n−1 2 , which is...