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68 relations: Affine sphere, Alexandroff extension, Ball (mathematics), Circle, Circle group, Closed set, Conformal geometry, Connected space, Constant curvature, Curse of dimensionality, Dimension, Disk (mathematics), Dover Publications, Embedding, Euclidean space, Exotic sphere, Gamma function, Gegenbauer polynomials, Hausdorff measure, Hodge star operator, Homeomorphism, Homology sphere, Homotopy groups of spheres, Homotopy sphere, Hopf fibration, Hyperbolic group, Hypercube, Hypersphere, Integral, Inversive geometry, Jacobian matrix and determinant, Leech lattice, Line segment, Loop (topology), Manifold, Mathematics, Möbius transformation, Natural number, Normal distribution, Octonion, Open set, Orthogonal group, Polar coordinate system, Prentice Hall, Quasigroup, Quaternionic projective space, Real number, Real projective line, Riemann sphere, Sign (mathematics), ..., Simply connected space, Sphere, Sphere packing, Spherical cap, Spherical coordinate system, Spherical harmonics, Spherical shell, Stereographic projection, Suspension (topology), Symplectic group, Topology, Torus, Uniform distribution (continuous), Volume element, Volume form, Volume of an n-ball, Wigner semicircle distribution, 3-sphere. Expand index (18 more) »
Affine sphere
In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point.
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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.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Circle
A circle is a simple closed shape.
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Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.
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Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
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Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Constant curvature
In mathematics, constant curvature is a concept from differential geometry.
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Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience.
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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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Disk (mathematics)
In geometry, a disk (also spelled disc).
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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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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Exotic sphere
In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Gegenbauer polynomials
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval with respect to the weight function (1 − x2)α–1/2.
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Hausdorff measure
In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in to each set in Rn or, more generally, in any metric space.
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Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
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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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Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1.
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Homotopy groups of spheres
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.
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Homotopy sphere
In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere.
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Hopf fibration
In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.
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Hyperbolic group
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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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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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Inversive geometry
In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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Loop (topology)
A loop in mathematics, in a topological space X is a continuous function f from the unit interval I.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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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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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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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.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Prentice Hall
Prentice Hall is a major educational publisher owned by Pearson plc.
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.
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Quaternionic projective space
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Real projective line
In geometry, a real projective line is an extension of the usual concept of line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity".
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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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Sign (mathematics)
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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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").
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Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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Spherical cap
In geometry, a spherical cap, spherical dome, or spherical segment of one base is a portion of a sphere cut off by a plane.
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Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
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Spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.
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Spherical shell
In geometry, a spherical shell is a generalization of an annulus to three dimensions.
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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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Suspension (topology)
In topology, the suspension SX of a topological space X is the quotient space: of the product of X with the unit interval I.
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Symplectic group
In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and, the latter is called the compact symplectic group.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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Uniform distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.
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Volume element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.
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Volume form
In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).
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Volume of an n-ball
In geometry, a ball is a region in space comprising all points within a fixed distance from a given point; that is, it is the region enclosed by a sphere or hypersphere.
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Wigner semicircle distribution
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse): for −R ≤ x ≤ R, and f(x).
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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References
[1] https://en.wikipedia.org/wiki/N-sphere
