# What is the 'center circle' of a Mobius Band?

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.