A note on a problem of Erdős on right angles (Q1045008)

\textit{P. Erdős} [Problems and results in combinatorial analysis, in: Proc. 8th southeast. Conf. on Combinatorics, graph theory, and computing; Baton Rouge 1977, 3--12 (1977; Zbl 0416.05059)] asked the question whether it is true that a set of \(n^2\) points in the plane always contains \(2n-2\) points which do not determine a right angle. Erdős proved that there always exists a subset of \(cn^{2/3}\) points with this property. The author of the paper shows that, apart from a log-factor, the answer to Erdős' question is in the affirmative. Moreover, he proves that the same holds for any angle \(\beta\in (0, \pi)\) in place of \(90^\circ\).