Möbius transformations

(redirected from Mobius transformations)

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.
Mathematically, the Mobius transformations guarantee the integrity of this movement.