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Hyperbolic geometry and Pseudosphere

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

Difference between Hyperbolic geometry and Pseudosphere

Hyperbolic geometry vs. Pseudosphere

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry. In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature.

Similarities between Hyperbolic geometry and Pseudosphere

Hyperbolic geometry and Pseudosphere have 10 things in common (in Unionpedia): Eugenio Beltrami, Gaussian curvature, Geometry, Hyperbolic geometry, Hyperbolic space, Hyperboloid, Hyperboloid model, Isometry, Minkowski space, Saddle point.

Eugenio Beltrami

Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics.

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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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Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

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Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.

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Hyperboloid model

In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+.

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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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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Saddle point

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes.

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The list above answers the following questions

Hyperbolic geometry and Pseudosphere Comparison

Hyperbolic geometry has 175 relations, while Pseudosphere has 33. As they have in common 10, the Jaccard index is 4.81% = 10 / (175 + 33).

References

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

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