n points in the plane can determine \(n^{3/2}\) unit circles (Q2266448)

The paper deals with the following problem of P. Erdős: Given n points in the plane (no three collinear) draw a circle through each triple. How many of these circles can have unit radius? Erdős proved for the maximal number f(n) of these circuits \(c_ 1n\leq f(n)\leq n(n-1)\) for some constant \(c_ 1\). The author improves the lower bound to \(c_ 2\geq n^{3/2}\) by constructing an appropriate set of n points.