November 17 - Happy Birthday, August Ferdinand Mobius

Posted on November 17, 2021

Key Points

This is an update of my post published on November 17, 2010:

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

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?

The field of mathematics that Mobius 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.