Editing August Ferdinand Möbius (section)

==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>