# Möbius transformations

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## Möbius transformations

[′mər·bē·əs ‚tranz·fər′mā·shənz]
(mathematics)
These are the most commonly used conformal mappings of the complex plane; their form is ƒ(z) = (az + b)/(cz + d) where the real numbers a, b, c, and d satisfy ad-bc ≠ 0. Also known as linear fractional transformations. Also known as bilinear transformations; homographic transformations.
References in periodicals archive ?
Exploring geometries associated with Mobius transformations of the hypercomplex plane, Kisil (U.
Lepton and quark approximate mass values are determined by the j-invariant function of elliptic modular functions, being related to the above subgroups and Mobius transformations in both discrete lattice spaces and continuous spaces.
Conservation laws in physics can be related to Mobius transformations in both discrete and continuous spaces.
In the limit when the node spacing approaches zero, the continuous approximation appears and the Mobius transformations include the continuous symmetry transformations.
AhB], [LV]) that such a map exists and is unique up to post-compositions with Mobius transformations.
It follows that up to post-compositions with Mobius transformations, f = [f.
It follows that [Mathematical Expression Omitted] is a group of Mobius transformations and an argument similar to Lemma 2.
These conformal transformations are called fractional linear transformations, or Mobius transformations, of the Riemann sphere, expressed by the general form [8]
The binary tetrahedral, octahedral and icosahedral rotation groups are the finite groups of Mobius transformations PSL(2, [Z.
then f is a Mobius transformation of g, two of the shared values, say [a.
o h o r f = T o g, where L, T are Mobius transformation, h is a non-constant entire function and
Then f is a Mobius transformation of g , two of the shared values, say [a.

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