# 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

### 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.

# Translation

#### Find a translation for the **mobius strip** definition in other languages:

Select another language:

#### Discuss these mobius strip definitions with the community:

# Citation

## Use the citation below to add this definition to your bibliography:

"mobius strip." *Definitions.net.* STANDS4 LLC, 2014. Web. 21 Sep. 2014. <http://www.definitions.net/definition/mobius strip>.