Similarities between Möbius transformation and Stereographic projection
Möbius transformation and Stereographic projection have 25 things in common (in Unionpedia): Alexandroff extension, Bijection, Complex analysis, Complex number, Conformal geometry, Conformal map, Geometry, Homeomorphism, Homogeneous coordinates, Hyperbolic geometry, Hyperplane, Isometry, Logarithmic spiral, N-sphere, Navigation, Poincaré disk model, Point at infinity, Projective geometry, Rational number, Rhumb line, Riemann sphere, Riemannian manifold, Sphere, Stereographic projection, Unit sphere.
Alexandroff extension
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.
Alexandroff extension and Möbius transformation · Alexandroff extension and Stereographic projection ·
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
Bijection and Möbius transformation · Bijection and Stereographic projection ·
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
Complex analysis and Möbius transformation · Complex analysis and Stereographic projection ·
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
Complex number and Möbius transformation · Complex number and Stereographic projection ·
Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.
Conformal geometry and Möbius transformation · Conformal geometry and Stereographic projection ·
Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
Conformal map and Möbius transformation · Conformal map and Stereographic projection ·
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.
Geometry and Möbius transformation · Geometry and Stereographic projection ·
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
Homeomorphism and Möbius transformation · Homeomorphism and Stereographic projection ·
Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.
Homogeneous coordinates and Möbius transformation · Homogeneous coordinates and Stereographic projection ·
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
Hyperbolic geometry and Möbius transformation · Hyperbolic geometry and Stereographic projection ·
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
Hyperplane and Möbius transformation · Hyperplane and Stereographic projection ·
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
Isometry and Möbius transformation · Isometry and Stereographic projection ·
Logarithmic spiral
A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature.
Logarithmic spiral and Möbius transformation · Logarithmic spiral and Stereographic projection ·
N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
Möbius transformation and N-sphere · N-sphere and Stereographic projection ·
Navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.
Möbius transformation and Navigation · Navigation and Stereographic projection ·
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.
Möbius transformation and Poincaré disk model · Poincaré disk model and Stereographic projection ·
Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
Möbius transformation and Point at infinity · Point at infinity and Stereographic projection ·
Projective geometry
Projective geometry is a topic in mathematics.
Möbius transformation and Projective geometry · Projective geometry and Stereographic projection ·
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
Möbius transformation and Rational number · Rational number and Stereographic projection ·
Rhumb line
In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.
Möbius transformation and Rhumb line · Rhumb line and Stereographic projection ·
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.
Möbius transformation and Riemann sphere · Riemann sphere and Stereographic projection ·
Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
Möbius transformation and Riemannian manifold · Riemannian manifold and Stereographic projection ·
Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Möbius transformation and Sphere · Sphere and Stereographic projection ·
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
Möbius transformation and Stereographic projection · Stereographic projection and Stereographic projection ·
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.
Möbius transformation and Unit sphere · Stereographic projection and Unit sphere ·
The list above answers the following questions
- What Möbius transformation and Stereographic projection have in common
- What are the similarities between Möbius transformation and Stereographic projection
Möbius transformation and Stereographic projection Comparison
Möbius transformation has 158 relations, while Stereographic projection has 120. As they have in common 25, the Jaccard index is 8.99% = 25 / (158 + 120).
References
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