Abstract
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 ) .
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Received April 19, 1999, and in revised form February 29, 2000, and September 12, 2000. Online publication April 6, 2001.
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Braß, P., Rote, G. & Swanepoel, K. Triangles of Extremal Area or Perimeter in a Finite Planar Point Set. Discrete Comput Geom 26, 51–58 (2001). https://doi.org/10.1007/s00454-001-0010-6
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DOI: https://doi.org/10.1007/s00454-001-0010-6