Erdős Problem #827

The points of `S` lie on a circle of radius `r`.

Distinct triples of points of `S` never lie on circles of the same radius. For a set with no three collinear points, every triple lies on exactly one circle, so this says that the \(\binom{|S|}{3}\) circumradii are pairwise different.

\(n_k\): the least \(m\) such that every set of \(m\) points of \(\mathbb{R}^2\) in general position (no three collinear, no four concyclic) contains \(k\) points whose \(\binom{k}{3}\) triples determine circles of pairwise different radii. By [MaRo15] such an \(m\) exists for every \(k\), so `sInf` is a true minimum.