The smallest triangular cover for triangles of diameter one (Q1767367)

A convex region covers a family \(\mathcal{C}\) of curves if it contains a congruent copy of each curve from \(\mathcal{C}\). In this paper the authors determine the smallest triangle \(T\) similar to a given triangle \(T_0\) which covers the family of all triangles of diameter 1. An exhaustive discussion proves that there exist four triangle similar to \(T_0\) such that, depending on some relations between the angles of \(T_0\), the triangle \(T\) is one of them.