“Look at this brand new undershirt,” my wife said. “I am shaking it and shaking it but still I have this twist. Can you see what to do?”
I gave the undershirt a good shake. And another one. And one more. And then it struck me. It was a Möbius undershirt!
What a rare case in which mathematics can come to the rescue in domestic matters
“There is no way in the world this twist can be undone,” I said. “This is a mathematical fact! It is a Möbius undershirt!” My wife listened carefully to my firm statement.
I started to day-dream about the bright future of this rare Möbius undershirt: I will show her to my colleagues!, I will display her in public lectures, and even let some selected graduate students hold her. However, a few days later my Möbius undershirt disappeared. The open sewing machine may give a hint of what had happend.
Of course, I do not have a picture of a Möbius undershirt but only of an ordinary one. There is no way in the world an ordinary undershirt can be turned into a Möbius undershirt. This is a mathematical fact!
Combinatorics and more 
I once knitted a moebius scarf as a present… Don’t have a picture, though.
I assure you there is every way you can have a Mobius undershirt. All it takes is the seamstress/tailor matching underarm end with hem and hem with underarm, instead of hem with hem and underarm with underarm.
Don’t ask me how I know this…
🙂
In addition to its potential future for undershirts, a variety of things that incorporate the idea of the Moebius band have been patented!
Take a look at:
http://patft.uspto.gov/
and enter the search string:
moebius band
and then try on the pair:
moebius
typewriter
For the second you will find a variety of typewriter ribbon inventions that are based on the moebius band.
Try googling for Klein bottle hats. Many people make things like that on purpose.
=]