A Möbius strip is the result you get when you give one of the ends a twist of π radians, and you join the ends together. There are some cool properties of the Möbius strip: first of all, it has only one edge. So if a car was traveling on the edge of a Möbius strip, the car would cover both edges of the Möbius strip without crossing an edge. A Möbius strip also has one side. If you paint the surface of a Möbius strip, you would paint everything on the Möbius strip. Lastly, you cannot cut one in half. If you cut one in half, your shape you end up with has a twist of 4π radians.
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