Let $\pi$ be the set of points in a plane and $f : \pi \to \pi$ be a mapping such that the image of any triangle (as its polygonal line) is a square. Show that $f(\pi)$ is a square.
Source: Romania IMO TST 1992 p3
Tags: function, Triangle, algebra
Let $\pi$ be the set of points in a plane and $f : \pi \to \pi$ be a mapping such that the image of any triangle (as its polygonal line) is a square. Show that $f(\pi)$ is a square.