August Ferdinand Möbius
August Ferdinand Möbius (1790–1868)
17 November 1790|
Schulpforta, Electorate of Saxony
|Died||26 September 1868
|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
|Doctoral students||Otto Wilhelm Fiedler|
|Other notable students||Hermann Hankel|
|Known for||Möbius strip
Möbius inversion formula
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 plane, 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.
Möbius was born in Schulpforta, Saxony-Anhalt, and was descended on his mother's side from religious reformer Martin Luther. He studied mathematics under Carl Friedrich Gauss and Johann Pfaff. Möbius died in Leipzig in 1868 at the age of 77. His son Theodor was a noted philologist.
- 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)
|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.
- 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.