A RAT-free (``right angle triangle-free'') set is a set of points, no three of which determine a Right Triangle. Let
be the largest integer such that a RAT-free subset of size is guaranteed to be contained in any set of
coplanar points. Then the function is bounded by

**References**

Abbott, H. L. ``On a Conjecture of Erdös and Silverman in Combinatorial Geometry.'' *J. Combin. Th. A* **29**, 380-381, 1980.

Chan, W. K. ``On the Largest RAT-FREE Subset of a Finite Set of Points.'' *Pi Mu Epsilon* **8**, 357-367, 1987.

Honsberger, R. *More Mathematical Morsels.* Washington, DC: Math. Assoc. Amer., pp. 250-251, 1991.

Seidenberg, A. ``A Simple Proof of a Theorem of Erdös and Szekeres.'' *J. London Math. Soc.* **34**, 352, 1959.

© 1996-9

1999-05-25