The topology of the Möbius strip
Here is a Möbius strip that you can rotate and zoom with your
This picture should help you to understand the definition of the
Möbius strip. It is swept out by the blue line as the green
circle rotates around the z-axis. While the circle makes a full
rotation, the line makes only half a turn.
This picture shows that the Möbius strip is homotopy equivalent
to the circle.