August Ferdinand Möbius
August Möbius  

August Ferdinand Möbius (1790–1868)


Born  Schulpforta, Electorate of Saxony 
17 November 1790
Died  26 September 1868 Leipzig 
(aged 77)
Residence  Germany 
Nationality  Saxon 
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: [ˈmøːbi̯ʊs]; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.
Early life and education
Möbius was born in Schulpforta, SaxonyAnhalt, and was descended on his mother's side from religious reformer Martin Luther.^{[1]} He was homeschooled until he was 13 when attended the College in Schulpforta in 1803 and studied there graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer, Karl Mollweide.^{[2]} In 1813 he began to study astronomy under the mathematically inclined professor Carl Friedrich Gauss at the University of Göttingen while Gauss was the director of the Göttingen Observatory. From there he went to study with Carl Gauss's instructor, Johann Pfaff at the University of Halle, where he completed his doctoral thesis The occultation of fixed stars in 1815.^{[3]} In 1816 he was appointed as Extraordinary Professor to the "chair of astronomy and higher mechanics" at the University of Leipzig.^{[4]} Möbius died in Leipzig in 1868 at the age of 77. His son Theodor was a noted philologist.
Contributions
He is best known for his discovery of the Möbius strip, a nonorientable twodimensional surface with only one side when embedded in threedimensional 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.^{[5]}
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)
References
 ↑ Szpiro, George (2007). Poincaré's Prize: The HundredYear Quest to Solve One of Math's Greatest Puzzles. Plume. p. 66. ISBN 9780525950240.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ August Ferdinand Möbius, The MacTutor History of Mathematics archive
 ↑ August Ferdinand Möbius, The MacTutor History of Mathematics archive
 ↑ August Ferdinand Möbius, The MacTutor History of Mathematics archive
 ↑ Howard Eves, A Survey of Geometry (1963), p. 64 (Revised edition 1972, Allyn & Bacon, ISBN 0205032265)
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<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 August Ferdinand Möbius at the Mathematics Genealogy Project
 August Ferdinand Möbius  Œuvres complètes GallicaMath
 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.