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Hyperbolic geometry and Möbius transformation

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Hyperbolic geometry and Möbius transformation

Hyperbolic geometry vs. Möbius transformation

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry. In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

Similarities between Hyperbolic geometry and Möbius transformation

Hyperbolic geometry and Möbius transformation have 24 things in common (in Unionpedia): Cayley–Klein metric, Conformal map, Conic section, Cross-ratio, Felix Klein, Geometry, Harold Scott MacDonald Coxeter, Homothetic transformation, Hyperbola, Hyperbolic 3-manifold, Hyperbolic geometry, Hyperbolic space, Isometry, Kleinian group, Minkowski space, Orthogonal group, Poincaré disk model, Poincaré half-plane model, Projective geometry, Reflection (mathematics), Riemann sphere, Special relativity, Stereographic projection, Unit sphere.

Cayley–Klein metric

In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space is defined using a cross-ratio.

Cayley–Klein metric and Hyperbolic geometry · Cayley–Klein metric and Möbius transformation · See more »

Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

Conformal map and Hyperbolic geometry · Conformal map and Möbius transformation · See more »

Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

Conic section and Hyperbolic geometry · Conic section and Möbius transformation · See more »

Cross-ratio

In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line.

Cross-ratio and Hyperbolic geometry · Cross-ratio and Möbius transformation · See more »

Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

Harold Scott MacDonald Coxeter and Hyperbolic geometry · Harold Scott MacDonald Coxeter and Möbius transformation · See more »

Homothetic transformation

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.

Homothetic transformation and Hyperbolic geometry · Homothetic transformation and Möbius transformation · See more »

Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

Hyperbola and Hyperbolic geometry · Hyperbola and Möbius transformation · See more »

Hyperbolic 3-manifold

In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1.

Hyperbolic 3-manifold and Hyperbolic geometry · Hyperbolic 3-manifold and Möbius transformation · See more »

Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

Hyperbolic geometry and Hyperbolic geometry · Hyperbolic geometry and Möbius transformation · See more »

Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

Hyperbolic geometry and Hyperbolic space · Hyperbolic space and Möbius transformation · See more »

Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.

Hyperbolic geometry and Isometry · Isometry and Möbius transformation · See more »

Kleinian group

In mathematics, a Kleinian group is a discrete subgroup of PSL(2, '''C''').

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

Hyperbolic geometry and Orthogonal group · Möbius transformation and Orthogonal group · See more »

Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.

Hyperbolic geometry and Poincaré disk model · Möbius transformation and Poincaré disk model · See more »

Poincaré half-plane model

In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H \, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.

Hyperbolic geometry and Poincaré half-plane model · Möbius transformation and Poincaré half-plane model · See more »

Projective geometry

Projective geometry is a topic in mathematics.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

Hyperbolic geometry and Reflection (mathematics) · Möbius transformation and Reflection (mathematics) · See more »

Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

Hyperbolic geometry and Riemann sphere · Möbius transformation and Riemann sphere · See more »

Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

Hyperbolic geometry and Special relativity · Möbius transformation and Special relativity · See more »

Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

Hyperbolic geometry and Stereographic projection · Möbius transformation and Stereographic projection · See more »

Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

Hyperbolic geometry and Unit sphere · Möbius transformation and Unit sphere · See more »

The list above answers the following questions

Hyperbolic geometry and Möbius transformation Comparison

Hyperbolic geometry has 175 relations, while Möbius transformation has 158. As they have in common 24, the Jaccard index is 7.21% = 24 / (175 + 158).

References

This article shows the relationship between Hyperbolic geometry and Möbius transformation. To access each article from which the information was extracted, please visit:

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