# Möbius Strip

A Möbius strip is a twisted surface in space that is made by starting with a rectangular piece of **paper**, twisting one side through 180° (relative to the opposite side), and then joining it to the opposite side. That is,
using the
**rectangle** shown in Figure 1, AC is joined to DB so that the point A coincides with the point D and the point C coincides with the point B.

It is a one-sided surface. That is, any point P on it can be joined to its opposite, Q (or to any other point) by a path that does not cross the edge of the surface. It is named after the nineteenth century mathematician, August Möbius.

If a Möbius strip is cut length-wise the result will be just one two sided surface. If cut again, the result will be two interconnected surfaces that, again, are two sided.

## Resources

### Books

Courant, Richard, and Herbert Robbins. *What Is Mathematics?* Oxford: Oxford University Press, 1948.

Smith, Karl J. *The Nature of Modern Mathematics.* Belmont, CA: Wadsworth Publishing Company, 1973.

Roy Dubisch

## Additional topics

Science EncyclopediaScience & Philosophy: *Linear expansivity* to *Macrocosm and microcosm*