The Optimal Twisted Paper Cylinder
An embedded twisted paper cylinder of aspect ratio $λ$ is a smooth isometric embedding of a flat $λ\times 1$ cylinder into $\R^3$ such that the images of the boundary components are linked. We prove that for such an object to exist we must have $λ>2$ and that this bound is sharp. We also show that any sequence of examples having aspect ratio converging to $2$ must converge to a (non-smooth) $4$-fold wrapping of a right-angled isosceles triangle.
math.MG↗