Möbius strip

The Moebius strip (named after the German mathematician August Ferdinand Moebius) is a topological object with only one surface and only one side. It is sometimes called a Moebius band.

A model can easily be created by taking a strip of material and giving it a half-twist, and then merging the ends of the strip together to form a single strip. It has a lot of curious properties. If you cut down the middle of the strip, instead of getting two separate strips, it becomes one long strip with four half-twists in it. If you cut this one down the middle, you get two strips wound around each other. alternatively, if you cut about a third of the way in from the edge you will get two strips; one is a thinner Moebius strip, the other is a long strip with four twists in it. Other interesting combinations of strips can be obtained by making Moebius strips with two ore more flips in them instead of one.

The Moebius strip has provided inspiration both for sculptures and for graphical art. Maurits C. Escher is one of the artists who was especially fond of it and based a great many of his litographies on this mathematical object.

It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke's The Wall of Darkness.

There have been technical applications; giant Moebius Strips have been used as conveyor belts (to make them last longer, since "each side" gets the same amount of wear) and as continuous-loop recording tapes (to double the playing time).

The 3D version of the Moebius Strip is the Klein bottle.