Experiment #1
See what happens with the untwisted loop first. Take a pencil or pen, and holding the loop on the table, draw a little star or square to indicate where you will start drawing. Then hold your pencil in placedo not lift the pencil off the tableas you drag the loop around. Keep going until you reach the little star or square you drew in the beginning.
Now look at the paper. Do all sides of the strip have your pencil markings? No. This, according to topology, proves that the loop is twosided. To get the pencil marking on the other side of the paper, you would have had to lift the pencil point off the table and turn the loop over.
OK. Now pick up the loop of paper that you twisted (this one is the Mobius strip). Go through the same procedure: draw a little star or square so that you can always see where you started. Keeping the pencil down and moving the loop under the pencil, keep going until you come back to the little star or square. Now look at the loop. Is there a side with no pencil marking? If not, then the strip has only one side!!
Experiment #2
Take the twosided loop of paper and carefully cut it in half. Perform the sidedness test on each half. What is the result?
Now take the onesided loop and carefully cut it in half. Perform the sidedness test on each half. What is the result?
If you want to keep going, make another Mobius strip only this time, cut it in thirds. What is the result?
Neat, huh?
