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Totally One-sided
By Linda | March 15, 2008
Here’s a quick trick to play on your friends and some pretty cool science to know. Cut a 2″ wide strip off the side of a standard letter size sheet of paper so that you have a strip of paper that is 2″ wide and 11″ long. Now ask someone if they can draw a continuous pencil line down the center of both sides of the strip without crossing an edge. It can be done.
Give up? You can accomplish the above chore by creating a Möbius strip. A Möbius strip or Möbius band is defined as a surface with only one side and only one boundary component. It has the mathematical property of being non-orientable.
It sounds complicated but all you need to do to make one is give your strip of paper a half-twist, and then join the ends of the strip together to form a single strip. Now, draw a line right down the center of the strip and your pencil will travel smoothly across the strip to end up right at the point it started!
The line you drew will be 22″ long (twice as long as your strip) because you have drawn down the center of both sides of the paper - without ever crossing an edge!
Now, what do you suppose will happen if you cut along the line you just made? You’ll get two new Möbius strips, right? Wrong! Try it and see what happens.
Topics: Projects & Experiments, Science Factoids, The Petri Dish |
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