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The Möbius strip is made by rotating one of the ends of a 2D strip 180° and then glueing these together. I was wondering, how wide can the strip be? For example, can we still make a Möbius strip from a square? Making a Möbius strip by rotating the long sides of the strip seems impossible without stretching the strip.

And how will the strip look like if we let the width grow on "both" sides (of which there is actually one)?

Deschele Schilder
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    Related questions have been asked at https://math.stackexchange.com/questions/733922/constructing-a-m%C3%B6bius-strip-using-a-square-paper-is-it-possible and https://math.stackexchange.com/questions/1262075/shortest-smooth-paper-m%C3%B6bius-strip, but not fully answered. There's a useful survey at https://www.nature.com/articles/nmat1929, freely available at https://www.ucl.ac.uk/~ucesgvd/moebius.pdf – Chris Culter Jan 19 '23 at 18:13
  • There’s no principal limit - unless you intend to embed the Möbius strip in $\Bbb R^3$. – Hagen von Eitzen Jan 19 '23 at 19:09
  • If you do, then this is an open problem. – mathlander Jan 20 '23 at 00:25
  • Recently solved by Richard Evan Schwartz. See my answer at https://math.stackexchange.com/q/4794888 – Gerry Myerson Oct 27 '23 at 02:19

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