A MOBIUS is...
The Möbius strip or Möbius band is a surface with only one side and only one boundary component. It has the mathematical property of being non-orientable. It is also a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.
A model can easily be created by taking a paper strip and giving it a half-twist, and then merging the ends of the strip together to form a single strip. In Euclidean space there are in fact two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise.
A closely related 'strange' geometrical object is the Klein bottle. The Klein bottle was first described in 1882 by the German mathematician Felix Klein.
The Möbius strip has provided inspiration both for sculptures and for graphical art. The artist M. C. Escher was especially fond of it and based several of his lithographs on it. One famous example, Möbius Strip II, features ants crawling around the surface of a Möbius strip. |
There have been technical applications. Giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time). Möbius strips are common in the manufacture of fabric computer printer and typewriter ribbons, as they allow the ribbon to be twice as wide as the printhead whilst using both half-edges evenly.
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