Look up hyperbolic in Wiktionary, the free dictionary.
Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.
The following phenomena are described as hyperbolic because they manifest hyperbolas, not because something about them is exaggerated.
Hyperbolic angle, an unbounded variable referring to a hyperbola instead of a circle
Hyperbolic coordinates, location by geometric mean and hyperbolic angle in quadrant I
Hyperbolic distribution, a probability distribution characterized by the logarithm of the probability density function being a hyperbola
Hyperbolic equilibrium point, a fixed point that does not have any center manifolds
Hyperbolic function, an analog of an ordinary trigonometric or circular function
Hyperbolic geometric graph, a random network generated by connecting nearby points sprinkled in a hyperbolic space
Hyperbolic geometry, a non-Euclidean geometry
Hyperbolic group, a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic geometry
Hyperbolic growth, growth of a quantity toward a finite-time singularity
Hyperbolic logarithm, original designation of natural logarithm (1647–1748) before Euler's formulation with e
Hyperbolic manifold, a complete Riemannian n-manifold of constant sectional curvature −1
Hyperbolic motion, an isometry in a hyperbolic space
Hyperbolic navigation, a class of radio navigation systems based on the difference in timing between the reception of two signals, without reference to a common clock
Hyperbolic number, a synonym for split-complex number
Hyperbolic orthogonality, an orthogonality found in pseudo-Euclidean space
Hyperbolic paraboloid, a doubly ruled surface shaped like a saddle
Hyperbolic partial differential equation, a partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives
Hyperbolic plane can refer to:
The 2-dimensional plane in hyperbolic geometry (a non-Euclidean geometry)
The hyperbolic plane as isotropic quadratic form
Hyperbolic quaternions, a non-associative algebra, precursor to Minkowski space
Hyperbolic rotation, a synonym for squeeze mapping
Hyperbolic sector, a planar region demarcated by radial lines and a hyperbola
Hyperbolic soccerball, a tessellation of the hyperbolic plane
Hyperbolic space, hyperbolic spatial geometry in which every point is a saddle point
Hyperbolic trajectory, a Kepler orbit with eccentricity greater than 1
Hyperbolic versor, a versor parameterized by a hyperbolic angle
Hyperbolic unit, a non-real quantity with square equal to +1
Look up hyperbolic in Wiktionary, the free dictionary. Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve)...
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than...
In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...
In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane...
plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines...
In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis...
precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group...
finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function 1 / x {\displaystyle 1/x}...
Circular orbit: e = 0 Elliptic orbit: 0 < e < 1 Parabolic trajectory: e = 1 Hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red...
The hyperbolic distribution is a continuous probability distribution characterized by the logarithm of the probability density function being a hyperbola...
In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles...
A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a)...
Hyperbole (/haɪˈpɜːrbəli/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is the use of exaggeration as a rhetorical device or figure of speech. In rhetoric, it is...
dynamical systems theory, a subset Λ of a smooth manifold M is said to have a hyperbolic structure with respect to a smooth map f if its tangent bundle may be...
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...
This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank....
hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic...
approximating integrals Maximum and minimum Derivative test Hyperbolic equilibrium point Hyperbolic geometry Minimax theorem Max–min inequality Monkey saddle...
A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals...
relatively hyperbolic groups are the fundamental groups of complete noncompact hyperbolic manifolds of finite volume. A group G is relatively hyperbolic with...
systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds. Near a hyperbolic point the...
In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane { ( x , y ) : x > 0 , y > 0 } = Q {\displaystyle...
In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous...
In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called...
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