Mobius Strip

Look at a normal sheet of paper. Count the number of sides. There's two - a front and a back, right? Pretty typical.

Here's how you make a not-so-typical piece of paper.

Take a long, thin strip of paper... 4 cm by 24 cm, for example. Anything reasonably close will do. Give one end a half twist and then tape it together. It should look similar to this:

(except it doesn't have to be blue.)

What you now have is a one-sided, one-edged piece of paper called the Mobius strip. To see that it has only one side, try drawing a line along one side and continue until you end up where you started. Like this:

Now see if you can find the "other side"... the side without a line on it. You won't find the other side, because there isn't one!

To see that there is only one edge, use a different colored pencil or pen and draw a line along the edge on one side of the center line you drew. Eventually you will end up where you started, and you will see that there are lines along "both" edges of the Mobius strip.

But since you drew only one continuous line, there must be only one edge!

Now think about what would happen if you cut down the center of your Mobius strip. An ordinary paper ring cut in half would give you two seperate rings, right? However, if you cut down the center of a Mobius strip, instead you end up one ring twice as large as the original!

For another (different) unexpected result, try cutting the strip one-third of the distance from the edge. I won't discuss what happens here... from experience I have found that it is more enjoyable to be suprised. So have fun!

One last amusement... the ants below are walking on a Mobius strip. So even though one ant may be above or below another, they are still on the same side!

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