Vol. 4, No. 1, 2011

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On the maximum number of isosceles right triangles in a finite point set

Bernardo M. Ábrego, Silvia Fernández-Merchant and David B. Roberts

Vol. 4 (2011), No. 1, 27–42
Abstract

Let Q be a finite set of points in the plane. For any set P of points in the plane, SQ(P) denotes the number of similar copies of Q contained in P. For a fixed n, Erdős and Purdy asked for the maximum possible value of SQ(P), denoted by SQ(n), over all sets P of n points in the plane. We consider this problem when Q = is the set of vertices of an isosceles right triangle. We give exact solutions when n 9, and provide new upper and lower bounds for S(n).

Keywords
Erdős problems, similar triangles, isosceles right triangles
Mathematical Subject Classification 2000
Primary: 52C10
Secondary: 05C35
Milestones
Received: 14 January 2010
Revised: 27 February 2011
Accepted: 27 February 2011
Published: 22 September 2011

Communicated by Kenneth S. Berenhaut
Authors
Bernardo M. Ábrego
Department of Mathematics
California State University
18111 Nordhoff Street
Northridge, CA 91330-8313
United States
http://www.csun.edu/~ba70714
Silvia Fernández-Merchant
Department of Mathematics
California State University
18111 Nordhoff Street
Northridge, CA 91330-8313
United States
http://www.csun.edu/~sf70713
David B. Roberts
Department of Mathematics
California State University
18111 Nordhoff Street
Northridge, CA 91330-8313
United States