Line transversals to unit disks (Q1849444)

Remember that a line transversal to a family of compact convex sets of Euclidean space is a straight line which intersects every set of this family. The author proves that if \(\mathcal F\) is a finite family of disjoint unit disks in the plane such that every three of those disks have a line transversal, then there exists a line which intersects all but at most \(C=12\) sets of \(\mathcal F\). He also outlines how his method applied to a family of translates of any plane compact convex set gives an analogical result with \(C=47\). The paper recalls other such general estimates, the currently best of which gives \(C=22\).