On the Banach-Mazur's distance in the plane

摘要

In this short paper we give a proof that the Banach-Mazur distance between quadrilaterals and triangles is smaller than 2. We also study the Banach-Mazur distance between the regular pentagon and the triangle. We give a detailed proof about the Banach-Mazur distance between the regular pentagon and the triangle, which was previously observed by some others.