Speaking of cutting Möbius strips, I used to love making Möbius bagels [1]. Fair warning: your significant other will likely be unimpressed to discover that a gnarled bagel is the "special surprise" you promised for breakfast.

[1] http://www.georgehart.com/bagel/bagel.html

I feel like I'm missing something. This feels like all set-up, with no reveal.

Is there more to the article, beyond the "Mobius Rip" section?

If anyone is talking about Mobius Strips then Cliff Stoll MUST be mentioned. This guys passion for Mobius Strips is infectious.

https://www.youtube.com/watch?v=AAsICMPwGPY

Also he was one of the first system admins to actually catch a hacker who was using his server in Germany in 1989. https://www.c-span.org/video/?10122-1/cuckoos-egg

If you glue those two pieces back together you get a single unbroken loop, not two circles. So, no, its not "easy to draw the circle segments so they don't intersect" because the lines won't form two circles