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20 relations: Beltrami–Klein model, Diffeomorphism, Differential geometry, Dimension, Euclidean space, Function (mathematics), Geodesic, Gnomonic projection, Homeomorphism, Hyperbolic geometry, Hypersphere, Identity function, Inverse function, Isometry, Mathematics, Poincaré disk model, Pseudo-Riemannian manifold, Radius, Riemannian manifold, Unit disk.
Beltrami–Klein model
In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere.
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Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
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Gnomonic projection
A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints.
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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.
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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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Hypersphere
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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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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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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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
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Radius
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
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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.
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Unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.
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