ABSTRACT
A Möbius strip Möbius strip is nonorientable. In addition, the Möbius strip in Figure 8.1 has only one side, as Escher’s ants are demonstrating. In general a surface lying in a three-manifold is called one-sided one-sided surface if a (three-dimensional!) ant can go for a walk along it and come back on the opposite side of the surface from which she started. It’s often thought that nonorientability and one-sidedness are just two aspects of the same property, but this is not the case, as you’ll discover in the following exercises.
