If you cut a Moebius strip in half down the middle, you obtain:
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A mathematician confided
That a Moebius strip is one-sided.
And you'll get quite a laugh
If you cut one in half
For it stays in one piece when divided.
[If you cut any strip with an odd number of half twists, say N, down the middle, you end up with a single strip half as wide with 2N + 2 half twists. But if you cut a strip with an even number of half twists down the middle, you get two linked strips.]