I have now created no less than six versions of the Moebius scarf by Cat Bordhi and I will never tire of this pattern , as it suits ALL yarns and textures, and is incredibly useful for remnants that have been breeding in your stash for years.

Euclidean geometry was one of my subjects in High School that maintained my interest beyond graduation and I thought I'd add the history of the Moebius strip from Wikipedia for your edification.

Leave it to a woman to take a complicated mathematical principal and convert it into something elegant and practical !

The Möbius strip or Möbius band (pronounced /ˈmøbiʊs/) 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 joining 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. The Möbius strip is therefore chiral, which is to say that it is "handed".

It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.

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. It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke's The Wall of Darkness. Science fiction stories sometimes suggest that our universe might be some kind of generalized Möbius strip. This is especially prominent in the Perry Rhodan-series. In the short story "A Subway Named Moebius", by A.J. Deutsch, the Boston subway authority builds a new line, but the system becomes so tangled that it turns into a Möbius strip, and trains start to disappear. The Möbius strip also features prominently in Brian Lumley's Necroscope series of novels.

A popular limerick is often associated with this design which reads 

"A mathematician confided

That a Möbius band is one-sided,

And you'll get quite a laugh,

If you cut one in half,

For it stays in one piece when divided"

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