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  2. Conformal geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Conformal_geometric_algebra

    In the algebra of this space, based on the geometric product of vectors, such transformations correspond to the algebra's characteristic sandwich operations, similar to the use of quaternions for spatial rotation in 3D, which combine very efficiently. A consequence of rotors representing transformations is that the representations of spheres ...

  3. Conformal geometry - Wikipedia

    en.wikipedia.org/wiki/Conformal_geometry

    Conformal geometry has a number of features which distinguish it from (pseudo-)Riemannian geometry. The first is that although in (pseudo-)Riemannian geometry one has a well-defined metric at each point, in conformal geometry one only has a class of metrics. Thus the length of a tangent vector cannot be defined, but the angle between two ...

  4. Conformal group - Wikipedia

    en.wikipedia.org/wiki/Conformal_group

    In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: The conformal orthogonal group.

  5. Liouville's theorem (conformal mappings) - Wikipedia

    en.wikipedia.org/wiki/Liouville's_theorem...

    In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, [1] is a rigidity theorem about conformal mappings in Euclidean space.It states that every smooth conformal mapping on a domain of R n, where n > 2, can be expressed as a composition of translations, similarities, orthogonal transformations and inversions: they are Möbius transformations (in n dimensions).

  6. Category:Conformal geometry - Wikipedia

    en.wikipedia.org/wiki/Category:Conformal_geometry

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  7. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space) and the conformal geometric algebra. Geometric calculus , an extension of GA that incorporates differentiation and integration , can be used to formulate other theories such as complex analysis and differential ...

  8. Conformal map - Wikipedia

    en.wikipedia.org/wiki/Conformal_map

    In plane geometry there are three types of angles that may be preserved in a conformal map. [3] Each is hosted by its own real algebra, ordinary complex numbers, split-complex numbers, and dual numbers. The conformal maps are described by linear fractional transformations in each case. [4]

  9. Geometric function theory - Wikipedia

    en.wikipedia.org/wiki/Geometric_function_theory

    A rectangular grid (top) and its image under a conformal map f (bottom). It is seen that f maps pairs of lines intersecting at 90° to pairs of curves still intersecting at 90°. A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane. More formally, a map,