4 problems

Let a paper Möbius band be a smooth isometric embedding of the flat Möbius band $M_{\lambda}$ in $\mathbb{R}^3$, and consider a sequence of smooth embedded paper Möbius bands whose…

An embedded paper Möbius band with $5$ or more half-twists is a paper Möbius band embedded in space with at least five half-twists; its aspect ratio is the ratio of its length to i…

A multi-twist paper Möbius band is a paper Möbius band with arbitrarily many half-twists, and its aspect ratio is the ratio of its length to its width. Schwartz–Neinhaus conjecture…

Let $K$ be a folded ribbon trefoil knot that is topologically a Möbius band, and let $\operatorname{Rib}([K]_{\mathrm{Möb}})$ denote its infimal folded ribbonlength in the Möbius-b…