physics. Möbius geometries and their transformations generalize this case to any number of dimensions over other fields. Möbius transformations are named...

d, and z are complex numbers (in which case the transformation is also called a Möbius transformation), or more generally elements of a field. The invertibility...

named after him, including the Möbius plane, the Möbius transformations, important in projective geometry, and the Möbius transform of number theory. His...

locally conformal to a Möbius geometry, meaning that there exists an angle preserving local diffeomorphism from the manifold into a Möbius geometry. In two...

In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist...

Examples of Möbius transformations include dilations, rotations, translations, and complex inversion. In fact, any Möbius transformation can be written...

 C) (Möbius transformations) Projective transformation Fuchsian group Table of Lie groups Anosov flow Kisil, Vladimir V. (2012). Geometry of Möbius transformations...

exchanges the two quadratics with one another. A suitably chosen Möbius transformation can transform a quartic equation into a quadratic equation in the...

itself is conformal if and only if it is a Möbius transformation. The complex conjugate of a Möbius transformation preserves angles, but reverses the orientation...

are examples of Möbius transformations, which under composition of functions form the Mobius group PGL(2, C). The six transformations form a subgroup...

Look up Möbius in Wiktionary, the free dictionary. Moebius, Mœbius, Möbius or Mobius may refer to: August Ferdinand Möbius (1790–1868), German mathematician...

isomorphism to the Möbius group. The following table lists the six generators, in which The first column gives a generator of the flow under the Möbius action (after...

switch between continuous-time and discrete-time representations Möbius transformation (complex analysis): a rational function of the form f(z) = (az +...

polynomial. This is the partial order version of the Möbius formula, not the number theoretic. The Möbius inversion formula for partial orders is: g ( x )...

an operator similar to the derivative which is invariant under Möbius transformations. Thus, it occurs in the theory of the complex projective line, and...

bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used for converting a transfer function H a ( s ) {\displaystyle...

transforms of R2 ≃ C ≃ M, namely, they are examples of Möbius transformations. A general Möbius transformation is given by ζ ′ = α ζ + β γ ζ + δ , α δ − β γ ≠...

of a group of Möbius transformations known as a Kleinian group. For Euclidean symmetry transformations rather than Möbius transformations, in general,...

f} must be an analytic automorphism of the unit disc, given by a Möbius transformation mapping the unit disc to itself. An analogous statement on the upper...

hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective...

In mathematics, the classical Möbius plane (named after August Ferdinand Möbius) is the Euclidean plane supplemented by a single point at infinity. It...

Ferdinand Möbius. A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical...

shear); Projective transformations preserve collinearity; Each of these classes contains the previous one. Möbius transformations using complex coordinates...

orthogonal group. Conformal linear transformations are a special type of Möbius transformations (conformal transformations mapping circles to circles); the...

Möbius triangle, and corresponds to a non-overlapping tiling, and the symmetry group is called a triangle group. In the sphere there are three Möbius...

The group PSL(2,C) of Möbius transformations of X normalizes the Lie algebra g {\displaystyle {\mathfrak {g}}} . The transformation j(z) = −z−1 corresponding...

{\mathfrak {C}}} by the Möbius transformation H , {\displaystyle {\mathfrak {H}},} apply the inverse of the Möbius transformation G = H − 1 {\displaystyle...

Parabolic coordinates Parabolic cylindrical coordinates parabolic Möbius transformation Parabolic geometry (disambiguation) Parabolic spiral Parabolic line...

important example of such functions is the group of Möbius transformations (see Möbius transformation § Overview). The original formulation of infinitesimal...

let Vs={v  ∈  V :|v|<s}. A Möbius gyrovector space (Vs,  ⊕ {\displaystyle \oplus } ,  ⊗ {\displaystyle \otimes } ) is a Möbius gyrogroup (Vs,  ⊕ {\displaystyle...