Triangles in Extremal Area or Perimeter in a Finite Planar Point Set

Peter Braß
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin
email: brass@inf.fu-berlin.de

Günter Rote
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin
email: rote@inf.fu-berlin.de

Konrad J. Swanepoel
Department of Mathematics and Applied Mathematics
University of Pretoria 0002
email: konrad@math.up.ac.za

Report B 00-06
March 2000

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 Theta n².

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