# What does “möbius” (moebius) mean?

In Starcraft II there was a mission called The Moebius Factor. Unrelated to that, a new Futurama episode called Möbius Dick was recently released.

Does anyone have any idea what does the word mean? Either generally, or in connection with any of the aforementioned phrases.

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Moebius is also a pseudonym of the french comic artist Jean Giraud, who did the famous Incal series of SF comics. en.wikipedia.org/wiki/Jean_Giraud –  starblue Aug 5 '11 at 16:02

This refers to the 2D-3D crossover object known as a Möbius strip. From Wikipedia:

The Möbius strip or Möbius band (pronounced UK: /ˈmɜːbiəs/ or US: /ˈmoʊbiəs/ in English, [ˈmøːbi̯ʊs] in German) (alternatively written Mobius or Moebius in English) 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.

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I bet not even you would be able to define what you meant with '2D-3D crossover' (apart denoting that it is a surface; it certainly does not point to the fact that the object has only one side and I feel it is only a metaphor for 'beware: this is complex'). –  Unreason Aug 5 '11 at 10:29
The 2D-3D crossover, I believe it could be explained, relates to the making use of this shape in topological space, where it is both a 2-dimensional manifold, yet seen as / spliced into, or can be interpreted (through thought experiments, and whatnot) as 3-dimensional. It also has the interesting property of not being simply connected, but seeming so. –  Grant Thomas Aug 5 '11 at 10:46
@Unreason: Yes, I use metaphors. –  Robusto Aug 5 '11 at 11:00
@Mr. Disappointment - you are right, my beef however is that any surface is a two-dimensional topological manifold and I feel that this metaphor does not really help someone who has no knowledge of geometry (nor it would be appreciated by someone who know geometry). Still, I am making too much noise over this - the definition given after the introduction is well chosen. –  Unreason Aug 5 '11 at 12:12
This is topology, not geometry. –  BlueRaja - Danny Pflughoeft Aug 5 '11 at 13:33

The Futurama episode is a pun, combining Moby Dick (the famous white whale) with the mathematician August Möbius. The episode is about killing a space-whale, and Futurama episode-names are often geeky puns.

Möbius is by far most famous for his Möbius strip, a three-dimensional surface with only one side, and a popular cultural reference (in the States, at least, children are taught about Möbius strips in elementary school). However, that's not the only thing he's known for - for instance, in college-level mathematics, the Möbius function is very important in the study of the Riemann-Zeta function.

The Starcraft mission is referring to the Möebius Foundation, a fictional organization which plays an important role in the game's storyline. It actually has nothing to do with Möbius, other than likely being named after him simply because game-developers are often math geeks :P

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