The mysterious Mobius strip!
If you have a piece of paper, that paper will have two sides, right? If
you wanted to, you could color one side red and the other side blue,
couldn’t you? And even if you roll the paper into a tube, it still has
two sides—an inside and an outside.
But could you have a piece of paper that has only one side?
Well, let’s see. Get a piece of paper and cut off a long, narrow strip.
With a pencil, put an A at the left end of the strip, and a B at the
right
end. Now, turn the strip over, keeping the B on your right. Bring the
two ends together. Next, twist the B end and place the B on top of the
A. Tape the ends together with transparent tape. Put tape on both sides.
Now you have a loop with a half twist in it.
The loop looks as if it has two sides, doesn’t it? If you had a giant
loop, you and a friend could begin coloring each side—one side red and
the other side blue. But if you did, you would be amazed to find that
your colors would bump into each other! For this kind of loop actually
has only one side! Start coloring your small loop red and see for
yourself.
This kind of twisted loop is called a Mobius strip, after the man who
invented it. And it’s a strange and almost “magical” sort of toy that
you can do some surprising things with. For example, what do you think
would happen if you were to cut a Mobius strip straight down the middle?
Do you think you would get two loops? No, indeed! After you finish
cutting it
in “half,” you’ll find that you still have only one loop—but it is
twice as long as the one you started with!
A mathematician confided
That a Mobius strip is one-sided.
And you’ll get quite a laugh
If you cut one in half
For it stays in one piece when divided!
What do you think would happen if you cut that loop down the middle?
Well, try it and see!
