This is a puzzle from P. Winkler: "Show that, given any closed curve in the plane, there is a square containing the curve, all four sides of which touch the curve."
I was NOT able to solve it quickly (i.e. in less than 30 minutes :D), and then I was impatient and looked at the solution presented on the linked page (I regret it, because it ended the fun of searching for a solution). I would like to see different solutions, so guys please try to solve it without looking at the solution there. :D
Can you prove it? Please show your proof!