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Möbius strip ( Trivia # 9 )

on Wednesday, April 29, 2009

The Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip 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 joining the ends of the strip together to form a loop. In Euclidean space there are in fact two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. The Möbius strip is therefore chiral, which is to say that it has "handedness" (as in right-handed or left-handed).

A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having traversed both sides of the strip, without ever crossing an edge.

The Universal Recycling Symbol is a form of Möbius strip.


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