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enter image description here

I mostly hear that a flatlander becomes their mirror counterpart when they make a turn inside it. Though for that to happen, they need to be turned upside down. Does it not make a difference when they are turned upside down inside 2D world? If so, how?

Let's say there is a stick coming from below, the flatlander will see a stick coming from below at first, when they make a full turn inside the Möbius strip, they'll see it coming it from above. So how can we say that it does not make a difference?

Thank you in advance, this is my first question in Math Stackexchange so sorry if I made a mistake.

Hagen von Eitzen
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Deha Ortasarı
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    If yo rotated by 180° "in place" from the starting position, you will end up with the two gaps on top, as in the final position. However, the right gap will be on the left and vice versa. Do you see now that the final position is (locally) mirrored relative to the starting position? – Hagen von Eitzen Sep 15 '19 at 12:35
  • Not necessarily an answer, but an illuminating and entertaining visualization: https://www.youtube.com/watch?v=4mdEsouIXGM –  Sep 15 '19 at 13:11

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If you observe the front and the back of the creature and follow it like below then you will see that not only turns it up side down but its back gets to the front:

enter image description here

zoli
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  • Exactly, but in many pictures I see, they don't include the upside part and turn the final image 180 degrees. Just like here: https://lh6.googleusercontent.com/-PiYITbX_0Bc/TsT1id-wDlI/AAAAAAAAArc/fWIbAdgaXWA/s384/flatland4.png – Deha Ortasarı Sep 15 '19 at 13:05
  • @DehaOrtasarı: That I don't know, and could not explain. – zoli Sep 15 '19 at 13:07
  • it has to make 2 laps... one outside 1 inside. –  Sep 21 '19 at 20:50