Covering families of triangles (Q6057469)

The paper continues the research by \textit{J.-w. Park} and \textit{O. Cheong} [Comput. Geom. 92, Article ID 101686, 10 p. (2021; Zbl 1471.52017)]. By a cover for a family \(\mathcal{F}\) of sets in the plane the authors mean a set into which every set from \(\mathcal{F}\) can be isometrically moved. Theorem 1 of this paper says that the triangle with sides \(\sqrt 2\), \(1+ \sqrt 2\) and \(\sqrt 3\) is a smallest convex cover for the family of triangles contained in the half-disk of radius \(1\). In Theorem 2 the authors describe a triangle which is the unique smallest convex cover for the family of triangles contained in the unit square.