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

Brass, Peter and Rote, Gunter and Swanepoel, Konrad (2001) Triangles of extremal area or perimeter in a finite planar point set. Discrete and Computational Geometry, 26 (1). pp. 51-58. ISSN 0179-5376

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Identification Number: 10.1007/s00454-001-0010-6

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 ) .

Item Type: Article
Official URL: http://www.springer.com/math/numbers/journal/454
Additional Information: © 2009 Springer
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 09 Oct 2009 09:47
Last Modified: 01 Oct 2010 09:27
URI: http://eprints.lse.ac.uk/id/eprint/25409

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