The Möbius strip has a number of horrifying properties. For example, if you were to glue two together by their edges, you'd get a Klein bottle (good luck with that).
One thing you can do is cut the strip in half along the middle. You will end up with one strip that is twice as long as the original strip of paper:
I know you're dying to know what happens if you were to cut this new strip in half along the middle. Naturally, you get two strips wound around each other (duh!):
This makes a good paper necklace or ribbon. More importantly, your cat will love it:
She's clearly wondering what she did to deserve this.
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