August Ferdinand Möbius

August Möbius
August Ferdinand Möbius (1790–1868)
Born	(1790-11-17)November 17, 1790 Schulpforta, Saxony-Anhalt, Germany
Died	September 26, 1868(1868-09-26) (aged 77) Leipzig
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 (November 17, 1790 – September 26, 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

• Gesammelte Werke erster Band (v. 1) (Leipzig : S. Hirzel, 1885)
• Gesammelte Werke zweiter Band (v. 2) (Leipzig : S. Hirzel, 1885)
• Gesammelte Werke dritter Band (v. 3) (Leipzig : S. Hirzel, 1885)
• Gesammelte Werke vierter Band (v. 4) (Leipzig : S. Hirzel, 1885)

Tributes

• 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 hommage 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.

References

External links

Wikisource has the text of a 1920 Encyclopedia Americana article about August Ferdinand Möbius.

• O'Connor, John J.; Robertson, Edmund F., "August Ferdinand Möbius", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Mobius.html .
• August Ferdinand Möbius at the Mathematics Genealogy Project
• August Ferdinand Möbius - Œuvres complètes Gallica-Math
• A beautiful visualization of Möbius Transformations, created by mathematicians at the University of Minnesota is viewable at http://youtube.com/watch?v=JX3VmDgiFnY
• Middle School Mathematician Project Short biography of Mobius by middle school students.