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Hyperbolic geometry and Stereographic projection

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

Difference between Hyperbolic geometry and Stereographic projection

Hyperbolic geometry vs. Stereographic projection

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry. In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

Similarities between Hyperbolic geometry and Stereographic projection

Hyperbolic geometry and Stereographic projection have 18 things in common (in Unionpedia): American Mathematical Society, Angle, Cartesian coordinate system, Conformal map, Gaussian curvature, Geometry, Hyperbolic geometry, Isometry, Mathematics, Möbius transformation, Plane (geometry), Poincaré disk model, Projective geometry, Quadric, Riemann sphere, Stereographic projection, Unit circle, Unit sphere.

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Conformal map

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

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.

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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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Hyperbolic geometry

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

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Isometry

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

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Möbius transformation

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.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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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.

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Projective geometry

Projective geometry is a topic in mathematics.

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Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

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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.

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Stereographic projection

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

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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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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.

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The list above answers the following questions

Hyperbolic geometry and Stereographic projection Comparison

Hyperbolic geometry has 175 relations, while Stereographic projection has 120. As they have in common 18, the Jaccard index is 6.10% = 18 / (175 + 120).

References

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

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