# Definitions for **mobius strip**

### This page provides all possible meanings and translations of the word **mobius strip**

### Princeton's WordNet

Mobius strip(noun)

a continuous closed surface with only one side; formed from a rectangular strip by rotating one end 180 degrees and joining it with the other end

### GCIDE

Mobius strip(n.)

A mathematical object, or a physical representation of it, which is a two-dimensional sheet with only one surface. It is constructed or visualized as a rectangle, one end of which is held fixed while the opposite end is twisted through a 180 degree angle and joined to the fixed end. It is a two-dimensional object that can only exist in a three-dimensional space.

**Origin:** [From August F. Mbius, a German mathematician.]

### Freebase

Möbius strip

The Möbius strip or Möbius band, also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as 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 two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. That is to say, it is a chiral object with "handedness". The Möbius band is not a surface of only one geometry, such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the Möbius band as any surface that is topologically equivalent to this strip. Its boundary is a simple closed curve, i.e., topologically a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any closed rectangle with length L and width W can be glued to itself to make a Möbius band. Some of these can be smoothly modeled in 3-dimensional space, and others cannot. Yet another example is the complete open Möbius band. Topologically, this is slightly different from the more usual — closed — Möbius band, in that any open Möbius band has no boundary.

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