November 17, 2010

Happy Birthday, August Ferdinand Mobius

Born on this day in 1790, this German mathematician is famous for his discovery of the Mobius strip, pictured here.

This is a two-dimensional surface that has only one side. You can easily make a mobius strip by cutting a narrow strip of paper, twisting one end a half turn, and taping the ends together. If you ignore the fact that the paper has a tiny height (or third dimension), your paper strip is now a 2-D surface with only one side.

Does it seem like it really has two sides? Prove to yourself that there is only one:

Draw a line right down the middle of the mobius strip, continuing until you meet up with the place where you started.

You will see that the line is on “both sides” of the strip of paper. Because there really aren't “both sides,” but just one side.

Now, what will happen if you cut along the line you drew. Will you get two mobius strips?

Here is a picture of August Mobius. The field of mathematics that he helped to develop is called topology. This is the study of shapes and spatial properties of things, even when those things are deformed—bent or curved around or stretched. Don't get this field of math mixed up with the kind of topology that geologists talk about—the landforms that are marked on a topological map.

• For further ideas about the Mobius strip, check out Math Squad.  

• Check out this website to see the cool graphic that artist M.C. Escher drew of a Mobius strip.  Other experiments to try are included here... 

• If you need a visual aid to help you create a Mobius strip (and experiment with it), try this video. 

Aside from the very famous Escher prints linked to above, Mobius strips do occasionally pop up in pop culture. Here is a Mobius wedding ring and an Escher-esque mural, to give you just two examples.