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What is the 'center circle' of a Mobius band? The question I am working on asks me to cut (literally) a Mobius band in half 'along its center circle.'

What exactly does this mean? I know the plane model for a Mobius band is simply a square with top edge $A$ and bottom edge $A^{-1}$

I just need help interpreting the directions of the question to get started! Thanks in advance for the help!

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Take a look at this image, think about a Mobius band embedded in $\mathbb{R}^3$. Alternatively, looking at the plane model, take the center line of the square. enter image description here

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    $\begingroup$ Yes, that's exactly it! $\endgroup$
    – B. Mehta
    Apr 18, 2018 at 4:38

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