The Mobius strip is a topological device with many amazing properties. You can make one from a simple strip of paper.
To make your very own Mobius strip simply take a paper strip, giving it a half twist and then joining the ends together to form a loop.
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.
The Mystery of the Mobius
But what's so special about this strip? Try colouring
one side of your strip green and the other side yellow. You'll find that you just
end up colouring the whole thing a dull blue. Why is that? Because
the most amazing thing about the Mobius strip is that it only has one side.
A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip. This single continuous curve demonstrates that the Möbius strip has only one boundary.
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
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 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.
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!
What use is it?
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There have been several technical applications for the Mobius strip.
Giant Mobius strips have been used as conveyor belts that last longer because
the entire surface area of the belt gets the same amount of wear, and as
continuous-loop recording tapes (to double the playing time). Mobius strips are
common in the manufacture of fabric computer printer and typewriter ribbons, as
they allow the ribbon to be twice as wide as the print head while using both
halves evenly.
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| A Mobius Scarf |
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