Editing August Ferdinand Möbius

{{Short description|German mathematician and astronomer (1790–1868)}}
{{Infobox scientist
| name              = August Möbius
| image             = August Ferdinand Möbius.jpg
| caption           = 
| birth_name        = August Ferdinand Möbius
| birth_date        = {{birth date|df=y|1790|11|17}}
| birth_place       = [[Schulpforta]], [[Electorate of Saxony]], [[Holy Roman Empire]]
| death_date        = {{death date and age|df=y|1868|9|26|1790|11|17}}
| death_place       = [[Leipzig]], [[Kingdom of Saxony]], [[North German Confederation]]
| fields            = [[Mathematics]]
| workplaces        = University of Leipzig
| alma_mater        = {{ubl|[[University of Leipzig]]|[[University of Göttingen]]|[[University of Halle]]}}
| doctoral_advisor  = [[Johann Pfaff]]
| academic_advisors = {{ubl|[[Carl Friedrich Gauss]]|[[Karl Mollweide]]}}
| doctoral_students = [[Otto Wilhelm Fiedler]]
| notable_students  = [[Hermann Hankel]]
| known_for         = {{ubl|[[Möbius strip]]|[[Möbius transformation]]s|[[Möbius transform]]|[[Möbius function]]|[[Möbius inversion formula]]|[[Möbius configuration]]|[[Möbius–Kantor configuration]]|[[Möbius–Kantor graph]]}}
| influences        = 
| influenced        = 
| awards            = 
| signature         = <!--(filename only)-->
| footnotes         = 
}}

'''August Ferdinand Möbius''' ({{IPAc-en|UK|ˈ|m|ɜː|b|i|ə|s}}, {{IPAc-en|US|ˈ|m|eɪ|-|,_|ˈ|m|oʊ|-}};<ref>{{cite LPD|3}}</ref> {{IPA|de|ˈmøːbi̯ʊs|lang}}; 17&nbsp;November 1790 &ndash; 26&nbsp;September 1868) was a German [[mathematician]] and theoretical [[astronomer]].

==Life and education==
Möbius was born in [[Schulpforta]], [[Electorate of Saxony]], and was descended on his mother's side from religious reformer [[Martin Luther]].<ref>{{cite book |author=George Szpiro |authorlink=George Szpiro |title=Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles |year=2007 |publisher=[[Plume (publisher)|Plume]] |page=[https://archive.org/details/poincarsprizehun0000szpi/page/66 66] |isbn=978-0-525-95024-0 |url=https://archive.org/details/poincarsprizehun0000szpi/page/66 }}</ref> He was home-schooled until he was 13, when he 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]].<ref name="st-andrews1">{{cite book |title=August Ferdinand Möbius |publisher=University of St Andrews, Scotland |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Mobius.html |archive-url=https://web.archive.org/web/20160330205503/http://www-history.mcs.st-andrews.ac.uk/Biographies/Mobius.html |archive-date=30 March 2016}}</ref> In 1813, he began to study astronomy under mathematician [[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.<ref name="st-andrews1"/> In 1816, he was appointed  as Extraordinary Professor to the "chair of astronomy and higher mechanics" at the University of Leipzig.<ref name="st-andrews1"/> Möbius died in [[Leipzig]] in 1868 at the age of 77. 

His son [[Theodor Möbius|Theodor]] was a noted [[philology|philologist]].

==Contributions==
He is best known for his discovery of the [[Möbius strip]], a [[non-orientable]] two-dimensional surface with only one side when [[Embedding|embedded]] in three-dimensional [[Euclidean space]]. It was independently discovered by [[Johann Benedict Listing]] a few months earlier.<ref name="st-andrews1"/> 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]]. He is recognized for the introduction of the [[barycentric coordinate system]].<ref name=Hille>Hille, Einar. "Analytic Function Theory, Volume I", Second edition, fifth printing. Chelsea Publishing Company, New York, 1982,  {{ISBN|0-8284-0269-8}}, page 33, footnote 1</ref> Before 1853 and [[Schläfli]]'s discovery of the [[4-polytopes]], Möbius (with [[Arthur Cayley|Cayley]] and [[Hermann Grassmann|Grassmann]]) was one of only three other people who had also conceived of the possibility of geometry in more than three dimensions.<ref>{{Cite book | last=Coxeter | first=H.S.M. | author-link=Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=Regular Polytopes (book) | page=141}}</ref>

Many mathematical concepts are named after him, including the [[Möbius plane]], the [[Möbius transformation]]s, 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.<ref>[[Howard Eves]], A Survey of Geometry (1963), p. 64 (Revised edition 1972, Allyn & Bacon, {{ISBN|0-205-03226-5}})</ref>

==Collected works==
* [https://archive.org/details/gesammeltewerkeh01mbuoft Gesammelte Werke  erster Band (v. 1)]  (Leipzig : S. Hirzel, 1885)
* [https://archive.org/details/gesammeltewerkeh02mbuoft Gesammelte Werke  zweiter Band (v. 2)]  (Leipzig : S. Hirzel, 1885)
* [https://archive.org/details/gesammeltewerkeh03mbuoft Gesammelte Werke  dritter Band (v. 3)]  (Leipzig : S. Hirzel, 1885)
* [https://archive.org/details/gesammeltewerkeh04mbuoft Gesammelte Werke  vierter Band (v. 4)]  (Leipzig : S. Hirzel, 1885)
* [https://libserv.aip.org/ipac20/ipac.jsp?session=166914R337JA5.559738&profile=rev-all&source=~!horizon&view=subscriptionsummary&uri=full=3100006~!44266~!1&ri=25&aspect=subtab232&menu=search&ipp=20&spp=20&staffonly=&term=Die+Elemente+der+Mechanik&index=.GW&uindex=&aspect=subtab232&menu=search&ri=25 Die elemente der mechanik des himmels, auf neuem wege ohne hülfe höherer rechnungsarten dargestellt von August Ferdinand Möbius] (Leipzig, Weidmann'sche buchhandlung, 1843)
<gallery>
File:Mobius-1.jpg|1843 copy of ''Die Elemente der Mechanik des Himmels''
File:Mobius-2.jpg|Title page to a 1843 copy of ''Die Elemente der Mechanik des Himmels''
File:Mobius-3.jpg|First page to a 1843 copy of ''Die Elemente der Mechanik des Himmels''
</gallery>

==See also==
*[[Barycentric coordinate system]]
*[[Collineation]]
*[[Homogeneous coordinates]]
*[[Möbius counter]]
*[[Möbius plane]]

==References==
{{Reflist}}

==External links==
{{Commons category|August Ferdinand Möbius}}
{{Americana Poster|Moebius, August Ferdinand|August Ferdinand Möbius}}
{{Wikisource1911Enc|Möbius, August Ferdinand}}
* {{MacTutor Biography|id=Mobius}}
* {{MathGenealogy|id=35953}}
* [http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_MOBIUS__1 August Ferdinand Möbius - Œuvres complètes] Gallica-Math
* A beautiful visualization of Möbius Transformations, created by mathematicians at the University of Minnesota is viewable at https://www.youtube.com/watch?v=JX3VmDgiFnY
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{{DEFAULTSORT:Mobius, August Ferdinand}}
[[Category:1790 births]]
[[Category:1868 deaths]]
[[Category:People from Naumburg (Saale)]]
[[Category:19th-century German astronomers]]
[[Category:19th-century German mathematicians]]
[[Category:German number theorists]]
[[Category:German geometers]]
[[Category:Leipzig University alumni]]
[[Category:University of Göttingen alumni]]
[[Category:University of Halle alumni]]
[[Category:Academic staff of Leipzig University]]