103 search results - page 1 / 21 » An improved bound on the number of unit area triangles |
COMPGEOM
2009
ACM
13 years 11 months ago
2009
ACM
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...
COMPGEOM
2008
ACM
13 years 6 months ago
2008
ACM
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, ...
COMBINATORICS
2002
13 years 4 months ago
2002
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...
CAGD
2004
13 years 4 months ago
2004
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...
IPCO
2007
13 years 6 months ago
2007
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...