The smallest convex cover for triangles of perimeter two
The ``worm problem'' by Leo Moser asks for the region of smallest area which will accommodate every arc of length 1. There are various variants of this still unsolved problem and the authors consider the following: Find the smallest convex region in the plane which contains a congruent copy of every triangle of perimeter two. The authors show that the solution is a triangle and give its (unique) shape.
scientific article; zbMATH DE number 1505845