I used an arrow with L and R written on it and marked the starting point matching these sides. Then I slid the arrow along the strip until i got back to the starting point and L and R were still in the same orientation. Only when the arrow was at the starting point but on the other side of the strip they were reversed. What is it I don't understand about the reversing effect of the strip? Thank you for your explanations. Mauro.
2026-04-29 12:32:04.1777465924
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Möbius strip reversing effect not happening
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Only when the arrow was at the starting point but on the other side of the strip they were reversed.
This is exactly right. Your visual model actually has two different ways of keeping track of the orientation:
- Which side of the strip is your arrow drawn on?
- Which sides of the arrow are L and R located on?
Going around the strip happens to flip both of these.
A Möbius strip you make out of paper isn't really a Möbius strip: it is actually a torus, since paper is actually a three-dimensional solid. The flat face of the paper strip isn't a Möbius strip either: it is a cylinder.
The actual mathematical object you're supposed to envision from your paper model is that the same location on opposite sides of the sheet of paper is supposed to actually be the same point. It's the same way that we envision a flat sheet of paper being (part of) the Euclidean plane, rather than being two copies of the Euclidean plane, one on either side.
I don't think there is really anything you don't understand, it's just that the reversing effect happens to the strip as well as the arrow. So, after the arrow is slid one round along the strip L and R are reversed and the arrow is on the other side and after the arrow is slid two rounds L and R are back in place and the arrow is back on the initial side.
Compare this to a cylinder, where after one round, L and R are in place and the arrow is on the side it started.