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Möbius transformation
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== References == '''Specific''' {{reflist|40em}} '''General''' {{refbegin}} * {{citation |last1=Arnold |first1=Douglas N. |last2=Rogness |first2=Jonathan |year=2008 |title=Möbius Transformations Revealed | journal=Notices of the AMS |pages=1226–1231 |volume=55 |issue=10 |url=http://www-users.math.umn.edu/~arnold/papers/moebius.pdf }} * {{citation | first=Alan F.|last=Beardon | title=The Geometry of Discrete Groups | publisher=New York: Springer-Verlag | year=1995 | isbn=978-0-387-90788-8}} * {{citation | first=G. S. |last=Hall | title=Symmetries and Curvature Structure in General Relativity | publisher=Singapore: World Scientific | year=2004 | isbn=978-981-02-1051-9}} ''(See Chapter 6 for the classification, up to conjugacy, of the Lie subalgebras of the Lie algebra of the Lorentz group.)'' * {{citation | first=Svetlana|last=Katok |author-link=Svetlana Katok| title=Fuchsian Groups | publisher=Chicago:University of Chicago Press | year=1992 | isbn=978-0-226-42583-2}} ''See Chapter 2''. * {{citation | last = Klein | first = Felix | author-link = Felix Klein | title = Lectures on the icosahedron and the solution of equations of the fifth degree | year = 1913 | edition = 2nd | orig-year = 1st German ed. 1884 | location = London | publisher = Kegan Paul, Trench, Trübner, & Co. | translator-last = Morrice | translator-first = George Gavin | url = https://archive.org/details/in.ernet.dli.2015.217159/ }} translated from {{citation | last = Klein | first = Felix | display-authors = 0 | url = https://archive.org/details/vorlesungenuberd0000feli/ | year = 1884 | title = Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade |language=de |publisher=Teubner }} * {{citation | first=Konrad | last=Knopp | title=Elements of the Theory of Functions | publisher=New York: Dover | year=1952 | isbn=978-0-486-60154-0 | url-access=registration | url=https://archive.org/details/elementsoftheory00konr }} ''(See Chapters 3–5 of this classic book for a beautiful introduction to the Riemann sphere, stereographic projection, and Möbius transformations.)'' * {{citation | first1= David |last1=Mumford|author-link1=David Mumford|first2=Caroline|last2=Series |first3=David|last3=Wright | title=Indra's Pearls: The Vision of Felix Klein | year=2002 | publisher= Cambridge University Press | isbn= 978-0-521-35253-6|title-link=Indra's Pearls (book)}} ''(Aimed at non-mathematicians, provides an excellent exposition of theory and results, richly illustrated with diagrams.)'' * {{citation | first=Tristan|last=Needham | title=Visual Complex Analysis | publisher=Oxford: Clarendon Press | year=1997 | isbn=978-0-19-853446-4}} ''(See Chapter 3 for a beautifully illustrated introduction to Möbius transformations, including their classification up to conjugacy.)'' * {{citation|first1=Roger|last1=Penrose|author-link1=Roger Penrose|first2=Wolfgang|last2=Rindler|author-link2=Wolfgang Rindler|title=Spinors and space–time, Volume 1: Two-spinor calculus and relativistic fields|publisher=Cambridge University Press|year=1984|isbn=978-0-521-24527-2}} * {{citation|first1=Hans|last1=Schwerdtfeger|author-link1=Hans Schwerdtfeger|title= Geometry of Complex Numbers |title-link= Geometry of Complex Numbers|publisher=Dover|year=1979|isbn=978-0-486-63830-0}} ''(See Chapter 2 for an introduction to Möbius transformations.)'' * {{citation| title = Finite Möbius groups, minimal immersions of spheres, and moduli| first = Gábor| last = Tóth| year = 2002 }} {{refend}}
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