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!


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

  • $\begingroup$ Ah I see. The center line is the line separating black from white then? $\endgroup$ – coreyman317 Apr 18 '18 at 4:37
  • 1
    $\begingroup$ Yes, that's exactly it! $\endgroup$ – B. Mehta Apr 18 '18 at 4:38

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