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?

It's seems to be meant as a supplement to the author's much longer piece "A Fight to Fix Geometry’s Foundations"[1] that was published the same day.

That article links to this one in a sidebar.

1: https://www.quantamagazine.org/20170209-the-fight-to-fix-sym...

That article is a very interesting read, thanks!

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

...That's the point?

You can't create a global situation where there are no intersections (and two circles), because of the twist in the gluing process. But you can create the appearance of it by constructing pieces in the deconstructed space, and not properly analyzing the results when gluing.

Ah. So "it's easy to draw what appear to be the circle segments, but aren't".

You see when he said "the circle segments" I thought he meant "the circle segments" instead of "straight lines that do not belong to the circles we were discussing earlier".

Well, perhaps this is reading too much in to the language, but you actually draw the circle segments without them crossing, but the gluing to reconstruct the space doesn't permit the segments to be glued back in to the circles they were decomposed from.

So you can draw a decomposition of the shapes in the decomposed space which apparently satisfies the properties, but you run in to trouble when you try to glue those partial solutions back together -- in this case, you can't simultaneously reconstruct the space and the shapes.