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August Ferdinand Möbius

August Möbius
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 (German: ; 17 November 1790 – 26 September 1868) 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)


  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.  

External links

  •  .
  • 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
  • Middle School Mathematician Project Short biography of Mobius by middle school students.
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