## Peter Braß, Günter Rote, and Konrad J. Swanepoel:

# Triangles of extremal area or perimeter in a finite planar point set

*Discrete and Computational Geometry* **26** (2001), 51–58. doi:10.1007/s00454-001-0010-6*
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### Abstract

We show the following two results on a set of `n` points in the
plane, thus answering questions posed by Erdös and Purdy (1971): 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}).

Last update: August 15, 2017.