Faster access than browser!Similarities between Hyperbolic geometry and Hyperbolic space
Hyperbolic geometry and Hyperbolic space have 21 things in common (in Unionpedia): American Mathematical Monthly, Conformal map, Elliptic geometry, Euclidean geometry, Exponential growth, Geodesic, Homothetic transformation, Hyperbolic 3-manifold, Hyperbolic geometry, Hyperbolic manifold, Isometry, János Bolyai, Mathematics, Metric space, Minkowski space, Nikolai Lobachevsky, Parallel postulate, Poincaré half-plane model, Pseudosphere, Saddle point, Stereographic projection.
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
American Mathematical Monthly and Hyperbolic geometry · American Mathematical Monthly and Hyperbolic space ·
Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
Conformal map and Hyperbolic geometry · Conformal map and Hyperbolic space ·
Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
Elliptic geometry and Hyperbolic geometry · Elliptic geometry and Hyperbolic space ·
Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
Euclidean geometry and Hyperbolic geometry · Euclidean geometry and Hyperbolic space ·
Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
Exponential growth and Hyperbolic geometry · Exponential growth and Hyperbolic space ·
Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
Geodesic and Hyperbolic geometry · Geodesic and Hyperbolic space ·
Homothetic transformation
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.
Homothetic transformation and Hyperbolic geometry · Homothetic transformation and Hyperbolic space ·
Hyperbolic 3-manifold
In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1.
Hyperbolic 3-manifold and Hyperbolic geometry · Hyperbolic 3-manifold and Hyperbolic space ·
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
Hyperbolic geometry and Hyperbolic geometry · Hyperbolic geometry and Hyperbolic space ·
Hyperbolic manifold
In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension.
Hyperbolic geometry and Hyperbolic manifold · Hyperbolic manifold and Hyperbolic space ·
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
Hyperbolic geometry and Isometry · Hyperbolic space and Isometry ·
János Bolyai
János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.
Hyperbolic geometry and János Bolyai · Hyperbolic space and János Bolyai ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Hyperbolic geometry and Mathematics · Hyperbolic space and Mathematics ·
Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
Hyperbolic geometry and Metric space · Hyperbolic space and Metric space ·
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.
Hyperbolic geometry and Minkowski space · Hyperbolic space and Minkowski space ·
Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.
Hyperbolic geometry and Nikolai Lobachevsky · Hyperbolic space and Nikolai Lobachevsky ·
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.
Hyperbolic geometry and Parallel postulate · Hyperbolic space and Parallel postulate ·
Poincaré half-plane model
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H \, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.
Hyperbolic geometry and Poincaré half-plane model · Hyperbolic space and Poincaré half-plane model ·
Pseudosphere
In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature.
Hyperbolic geometry and Pseudosphere · Hyperbolic space and Pseudosphere ·
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.
Hyperbolic geometry and Saddle point · Hyperbolic space and Saddle point ·
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
Hyperbolic geometry and Stereographic projection · Hyperbolic space and Stereographic projection ·
The list above answers the following questions
- What Hyperbolic geometry and Hyperbolic space have in common
- What are the similarities between Hyperbolic geometry and Hyperbolic space
Hyperbolic geometry and Hyperbolic space Comparison
Hyperbolic geometry has 175 relations, while Hyperbolic space has 65. As they have in common 21, the Jaccard index is 8.75% = 21 / (175 + 65).
References
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