Summary: On the maximum number of isosceles
right triangles in a finite point set
Bernardo M. ŽAbrego, Silvia FernŽandez-Merchant,
and David B. Roberts
Department of Mathematics
California State University, Northridge,
18111 Nordhoff St, Northridge, CA 91330-8313.
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, Erdos
and Purdy asked to determine 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).
In the 1970s Paul Erdos and George Purdy [6, 7, 8] posed the question, "Given a finite set
of points Q, what is the maximum number of similar copies SQ(n) that can be determined