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Scouts' Activities Pages | |
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Things Aren't
Always What They Seem !
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| Back in the early 1800's, a German mathmetician and astronomer, Augustus Ferdinand Mobius, created a mysterious object which still fascinates the scholars today. That invention bears his name and is known as the "Mobius Strip". It is, in fact, a ONE-SIDED PIECE OF PAPER. | ||
| A Mobius Strip is quite easy to construct. Simply take a long strip of paper, bring the ends together, as if to make a loop, but before joining them together, give one end a single flip. You can then tape the ends together. (see fig. 1) |  |
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There are several curious properties to a mobius strip. One of the most obvious ones is that the strip has only one side. OK, maybe it's not so obvious at first. Once you've made your Mobius Strip, take a pencil or pen and start at any spot in the centre of the strip and start drawing a line down the centre of the strip. DON'T LIFT YOUR PENCIL OR PEN OFF OF THE STRIP. What did you discover? You ended up back where you started, didn't you? Without taking the pencil or pen off of the strip, you drew a single line and got back to where you started. The strip has only ONE side ! |
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If you think that was a great trick, think about this one for a minute before you try it. If the strip has only one side, can it be cut in half? Try it for yourself by taking a pair of scissors and cutting along the line that you drew above. Again, your cut will end up back where you started so you must have cut it in half, didn't you? (see fig. 2) In fact, you didn't. You still have a single strip, it's just twice the size. |
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Now for one final test. Make another Mobius Strip and draw two lines on it, cutting it into thirds (see fig. 3). Now take your scissors and cut along both of these lines. What did you get this time? |
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Are there any other interesting properties that you can discover about the Mobius Strip ? |
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