11 search results - page 1 / 3 » The Minimum Number of Distinct Areas of Triangles Determined... |
SIAMDM
2008
13 years 4 months ago
2008
We prove a conjecture of Erdos, Purdy, and Straus on the number of distinct areas of triangles determined by a set of n points in the plane. We show that if P is a set of n points...
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...
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, ...
SODA
1992
ACM
13 years 6 months ago
1992
ACM
Given a set P of n points in the plane, we wish to find a set Q P of k points for which the convex hull conv(Q) has the minimum area. We solve this, and the related problem of fi...
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...