I am interested to see that a story about the Moebius strip actually makes the news headlines today today (here). It cheers the heart of a would-be nerd when ever a Maths story hits the headlines.
For those of you who aren't so sure about it, you take a piece of heavy paper cut it into a strip about 2 or 3 cms wide. In fact make two.
With the first one simply fold the ends together and glue them or use sticky tape.
With the second one you do the same only this time you put one twist in it
You can then do a couple of things to test the qualities of the strip.
First get a pen and draw a line along the middle of the strip and keep going until you get back to where you started.
With the ordinary (untwisted) strip you will of course find that this draws a continuous line around one side.
With the Moebius (twisted) strip though, you draw a line twice as long and you find that when you get back to where you started there is actually no "other side". The strip appears to have only one side.
The second thing you can do is to then cut along the line you have drawn. The first strip will cut into two separate strips the same diameter as the original but half the width.
But the Moebius strip will end up as only one circle, twice the size of the original and half the width, it will still have a twist.
If you're really nerdy (and you can see that I have done this before) you can even experiment with two or more twists and see what happens.
Of course the mathematical explanation is bizarrely complicated. I don't pretend to understand it, but at least it's not a story about someone being blown up, and there may be some application for this curious property. But that may just be hype to justify such research into obscurity.