August Ferdinand Möbius

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August Möbius
August Ferdinand Möbius.png
August Ferdinand Möbius (1790–1868)
Born (1790-11-17)17 November 1790
Schulpforta, Electorate of Saxony
Died 26 September 1868(1868-09-26) (aged 77)
Residence Germany
Nationality German
Fields Mathematician
Institutions University of Leipzig
Alma mater University of Leipzig
University of Göttingen
University of Halle
Doctoral advisor Johann Pfaff
Other academic advisors Carl Friedrich Gauss
Karl Mollweide
Doctoral students Otto Wilhelm Fiedler
Other notable students Hermann Hankel
Known for Möbius strip
Möbius transformations
Möbius transform
Möbius function
Möbius inversion formula
Möbius–Kantor configuration
Möbius–Kantor graph

August Ferdinand Möbius (17 November 1790 – 26 September 1868; German pronunciation: [ˈmøːbi̯ʊs]) was a German mathematician and theoretical astronomer.

He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict Listing around the same time. The Möbius configuration, formed by two mutually inscribed tetrahedra, is also named after him. Möbius was the first to introduce homogeneous coordinates into projective geometry.

Many mathematical concepts are named after him, including the Möbius transformations, important in projective geometry, and the Möbius transform of number theory. His interest in number theory led to the important Möbius function μ(n) and the Möbius inversion formula. In Euclidean geometry, he systematically developed the use of signed angles and line segments as a way of simplifying and unifying results.[1]

Möbius was born in Schulpforta, Saxony-Anhalt, and was descended on his mother's side from religious reformer Martin Luther.[2] He studied mathematics under Carl Friedrich Gauss and Johann Pfaff. Möbius died in Leipzig in 1868 at the age of 77.

Collected works[edit]


  • In the 1982 novel 2010: Odyssey Two, Arthur C. Clarke's first sequel to 2001: A Space Odyssey, HAL 9000 is described by Dr. Chandra as being caught in a "Hofstadter–Möbius loop". The movie uses the term "H. Möbius loop".
  • The character of Johann Wilhelm Möbius—a particular scientist who tries to evade his own inventions by pretending to be insane—in Dürrenmatt's satiric drama The Physicists is named after him.
  • The crater Möbius on the Moon's far side is named for him.
  • The asteroid 28516 Möbius is also named after him.
  • There is a tribute in Serious Sam: The Second Encounter, in the form on the deathmatch map dm_mobius (which has since spawned various spin-offs such as in the Unreal Tournament series).
  • Möbius plays a pivotal part in Brian Lumley's Necroscope book series.
  • Comic author and comic artist Jean Giraud also worked under the Moebius pen name, in homage to him.
  • Mobius One is the main character in the game Ace Combat 4:Shattered Skies. His emblem consists of a modified Möbius strip with several folds.
  • In the continuity of both the Archie Sonic the Hedgehog comic book series and the Sonic the Hedgehog Saturday morning cartoon, the planet that Sonic and his allies live on (which is actually Earth 3,000 in the future) is called "Mobius".
  • In the "Fallout: New Vegas" add on "Old World Blues" the primary antagonist is named "Dr. Mobius."


  1. ^ Howard Eves, A Survey of Geometry (1963), p. 64 (Revised edition 1972, Allyn & Bacon, ISBN 0-205-03226-5)
  2. ^ Szpiro, George (2007). Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles. Plume. p. 66. ISBN 978-0-525-95024-0. 

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