I understand that, from a topological perspective, it is irrelevant whether we choose the quotient of the square $[0,1]\times [0,1]$ (by identifying points $(0,t)$ and $(1,1-t)$) or the quotient of the rectangle $[0,1]\times[0,a]$, $a>1$ (where the obvious points are identified), as a model of the Möbius strip. However, it seems pretty hard, if not impossible, to actually physically construct a Möbius stirp using a square like paper.
I wonder if it is possible to determine the least $a\geq 1$, such that he Möbius strip is physically constructible using a paper congruent to $[0,1]\times[0,a]$. I guess that this answer may depend on factors such as the size and the thickness of the paper that we use. This may be related to the mathematics of paper folding. Is there a general answer to this question, taking relevant qualities of a paper into account? Does anyone know of a source answering this question?