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Sphere and Stereographic projection

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

Difference between Sphere and Stereographic projection

Sphere vs. Stereographic projection

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

Similarities between Sphere and Stereographic projection

Sphere and Stereographic projection have 22 things in common (in Unionpedia): Angle, Antipodal point, Cartesian coordinate system, Circle of a sphere, Embedding, Equator, Euclidean space, Gaussian curvature, Geometry, Homeomorphism, Integral, Mathematics, Meridian (geography), Plane (geometry), Point at infinity, Real projective plane, Riemann sphere, Sphere, Spherical coordinate system, Surface (topology), Topology, Unit sphere.

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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Antipodal point

In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter.

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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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Circle of a sphere

A circle of a sphere is a circle that lies on a sphere.

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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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Equator

An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel).

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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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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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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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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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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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Meridian (geography)

A (geographical) meridian (or line of longitude) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points of equal longitude.

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Plane (geometry)

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

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Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

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Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

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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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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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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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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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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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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

Sphere and Stereographic projection Comparison

Sphere has 153 relations, while Stereographic projection has 120. As they have in common 22, the Jaccard index is 8.06% = 22 / (153 + 120).

References

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

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