Math Insight

Applet: A Möbius strip is not orientable

Applet: A Möbius strip is not orientable

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A Möbius strip is shown with a normal vector. If you drag the red point on the slider, the normal vector moves along the Möbius strip. Once you drag the slider half way, the normal vector has moved all the way around the surface. However, now the normal vector is pointing in the opposite direction. Since the normal vector didn't switch sides of the surface, you can see that Möbius strip actually has only one side. For this reason, the Möbius strip is not orientable.

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