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The Amazing Mobius Strip

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The Mobius strip is a topological device with many amazing properties. It can easily be made from a strip of paper and some glue.

To construct your very own Mobius strip simply take two rectangular strips of paper and identify the bottom edge with the top edge in reverse, so that each of the bottom corners is identified with the opposite top corner - that is, twist it once in the middle and glue the ends together.

You just made your very own Mobius strip - and what fun you'll have. You'll find that no matter how you twist or bend a Mobius strip (short of tearing it in two and glueing it back together again) you'll never be able to get rid of that twist and turn it into just a normal loop. If you want to sound really clever you can say that the Mobius strip is not topologically equivalent to a cylinder.

The Mystery of the Mobius

But what's so special about this strip? Well, try colouring one side of your strip red and the other side green. You'll find that you just end up colouring the whole thing a sort of swampy brown. Why is that? Because the most amazing thing about the Mobius strip is that it only has one side. Follow it round with your finger if you like, and you'll find you end up on the opposite side from where you started without going over the edge.

This is where the symbol for infinity comes from. The sideways figure 8 you see, meaning infinity, is actually supposed to represent a Mobius strip, since the Mobius strip goes on forever.

More Fun With Your Mobius

So what else can you do with your Mobius strip? Well, since they're so much fun, why don't we try to cut it in half to make two of them? Draw completely around the centreline of your strip. Remember that you won't need to lift the pen to do both sides. Then get a sharp knife or a pair of scissors and cut along the line. When you get back to the start of your cut after cutting all the way around the strip, you'll be able to take your two Mobius strips apart and give one to a friend.

Only kidding! The Mobius strip is much more tricky than that. You'll find that you can't cut your Mobius strip in two at all. You've still just got one long loop with a couple of extra twists thrown in for good measure.

Still not satisfied? Then try cutting it in two again. Do it the same way - all the way around the strip, and this time you really do get two strips. But the Mobius strip still has another trick up its topological sleeve. The two strips you now have are linked together!

Cut them in two and what have you got? Pretty much just a load of swampy brown confetti, so I guess its time to make a new Mobius strip and start the fun all over again.

The Final Twist

As if all that wasn't enough, there's one more piece of fun you can have with a Mobius strip. If you take a normal cylinder - albeit a bendy one, for instance made from foam rubber - and glue the two ends together you get a torus or doughnut. However, if you glue the two edges of a Mobius strip together you'll produce the even more exciting and mysterious Klein Bottle. However, do not become frustrated if you cannot construct this exciting vessel, since a true Klein Bottle can only exist in four dimensions...

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