# 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, Figure 2. Illustration by Hans & Cassidy. Courtesy of Gale Group. Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group. 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