Triangles of extremal area or perimeter in a finite planar point set.
Brass, P., Rote, G. & Swanepoel, K.
(2001).
Triangles of extremal area or perimeter in a finite planar point set.
Discrete and Computational Geometry,
26(1), 51-58.
https://doi.org/10.1007/s00454-001-0010-6
(2001).
Triangles of extremal area or perimeter in a finite planar point set.
Discrete and Computational Geometry,
26(1), 51-58.
https://doi.org/10.1007/s00454-001-0010-6
We show the following two results on a set of n points in the plane, thus answering questions posed by Erdos and Purdy [11]: 1. The maximum number of triangles of maximum area (or of maximum perimeter) in a set of n points in the plane is exactly n . 2. The maximum possible number of triangles of minimum positive area in a set of n points in the plane is Θ(n 2 ) .