How many edges does this piece of paper have? How many surfaces? Now twist one end and tape it onto the other end, making a Möbius strip. Now, trace the sides; how many sides? How many surfaces? How can you tell?

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Rubber sheet geometry says two objects are equivalent by distortion if we can stretch, shrink, bend, or twist one without cutting or gluing and deform it into the other. Review the shapes below. Are these two shapes equivalent by distortion or not, and why?

Möbius strips are fascinating. Try this at home. Get a piece of paper, scissors, and tape. Cut a strip of paper, maybe an inch wide. How many edges does this piece of paper have? How many surfaces? Now twist one end and tape it onto the other end, making a Möbius strip. Now, trace the sides; how many sides? How many surfaces? How can you tell?

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