There was a claim that a circle on a curved surface will always conain the vertices of a square that lie in one plane.
Differently put: You can always rotate a square table to find a position where it doesn't wobble.
There was a paper, I think — unfortunately I don't remember where I read it, nor whether it confirmed or refuted the claim.
I've done a couple of tests in cafeś — in case you see someone sitting at a diagonally rotated table in a café in Berlin.
