Vol. 4, No. 1, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11
Issue 2, 181–359
Issue 1, 1–179

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Addresses
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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