Pushing a rectangle down a path (Q666891)

A \textit{Jordan loop} is just any homeomorphic image of the unit circle $S^1$. It is known that, for ``good'' families of Jordan loops, Jordan loops always contain four points that are the vertices of a square. Some similar results are also known for different types of quadrilaterals. The paper considers results dealing with families of rectangles whose vertices lie in a given Jordan loop. In particular, the author provides results ``in the spirit of Gromov's famous nonsqueezing theorem from symplectic topology''.