4 problems

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…

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…

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…

Let $M_{\lambda}=([0,1]\times[0,\lambda])/\sim$ be the flat Möbius band, where $(x,0)\sim(1-x,\lambda)$, and let a paper Möbius band be a smooth isometric embedding…