Word.ws English Dictionary

Möbius transformation

Möbius transformation noun: a transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.

Noun

Möbius transformation (plural Möbius transformations)

  1. A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.
    • Jørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete.2008, J. Vernon Armitage, John Parker, Jørgensen's inequality for Non-Archimedean Metric Spaces, Mikhail Kapranov, Sergii Kolyada, Yu. I. Manin, Pieter Moree, Leonid Potyagailo (editors), Geometry...
    • Modular Möbius number systems consist of Möbius transformations with integer coefficients and unit determinant.2012, Martin Delacourt, Petr Kůrka, Finite State Transducers of Modular Möbius Number Systems, Branislav Rovan, Vladimiro Sassone, Peter Widmayer (editors), Mathematical Foundations of Computer...

Forms of Möbius transformation

pluralMöbius transformations
alternative formMobius transformation
alternative formMoebius transformation

Origin of Möbius transformation

Named for German mathematician and theoretical astronomer August Ferdinand Möbius (1790–1868).

Questions about Möbius transformation

What does Möbius transformation mean?
Möbius transformation means a transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.
What part of speech is Möbius transformation?
Möbius transformation is a noun.
What is the plural of Möbius transformation?
The plural of Möbius transformation is Möbius transformations.

Words near Möbius transformation in the dictionary

  1. Möbius scarf
  2. Möbius scarves
  3. Möbius strip
  4. Möbius strips
  5. Möbius syndrome
  6. Möbius transformation
  7. Möbius transformations
  8. Möller-Barlow disease
  9. Mölndal
  10. Mönchengladbach
  11. Möngke

Source and license

Adapted from Wiktionary: Möbius transformation (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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