Moebius

Moebius, often spelled Möbius, is a name used in mathematics, science, and culture, and as a pseudonym in comics. It is most commonly associated with mathematical concepts named after August Ferdinand Möbius, and with the French artist Jean Giraud, who published under the pen name Moebius.

In mathematics, Moebius names three related ideas. The Möbius strip is a non-orientable surface with one side and one boundary component, discovered in 1858 by Möbius and Listing. The Möbius function mu(n) is an arithmetic function used in number theory, defined by mu(1)=1, mu(n)=(-1)^k if n is a product of k distinct primes, and mu(n)=0 if n has a squared prime factor. Möbius transformations are fractional linear maps f(z)=(az+b)/(cz+d) with ad-bc ≠ 0 that act on the extended complex plane and preserve angles locally; they form a group of conformal automorphisms of the Riemann sphere.

Jean Giraud (1938–2012) worked under the pseudonym Moebius for much of his science fiction and fantasy art. He produced influential comics such as Arzach and The Airtight Garage and contributed to Metal Hurlant. He also co-created The Incal with writer Alejandro Jodorowsky.

Outside mathematics and comics, Moebius is a surname of German origin, and the form Möbius is used in many technical terms and academic disciplines. The spelling without the diaeresis is common in English-language usage.