Strip Tease...

The Möbius strip of course...

I suspect we all think we've read enough about Möbius strips in the last many years (decades?)... but I'd encourage folks to make time for Evelyn Lamb's current read on the topic (one of her "favorite spaces"):

http://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-the-moebius-strip/

She relates it back to the four-color-theorem, which is not often done (or six-color-theorem in this case). And these days, if you're expounding on Möbius strips, it's almost obligatory to include Vi Hart's story based on the same. I'm happy to report that Dr. Lamb does so at the end.