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.
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.
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