Hyperbolic
Encyclopedia
Hyperbolic refers to something related to or in shape of hyperbola
(a type of curve), or to something employing the literary device of hyperbole
(overstatement or plausible exaggeration).
The following topics are based on the hyperbola etymology:
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
(a type of curve), or to something employing the literary device of hyperbole
Hyperbole
Hyperbole is the use of exaggeration as a rhetorical device or figure of speech. It may be used to evoke strong feelings or to create a strong impression, but is not meant to be taken literally....
(overstatement or plausible exaggeration).
The following topics are based on the hyperbola etymology:
- Hyperbolic functionHyperbolic functionIn mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" , and the hyperbolic cosine "cosh" , from which are derived the hyperbolic tangent "tanh" and so on.Just as the points form a...
- Hyperbolic geometryHyperbolic geometryIn mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
- Hyperbolic groupHyperbolic groupIn group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic geometry. The notion of a hyperbolic group was introduced...
- Hyperbolic growthHyperbolic growthWhen a quantity grows towards a singularity under a finite variation it is said to undergo hyperbolic growth.More precisely, the reciprocal function 1/x has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x \to 0 is infinity: any similar graph is said to exhibit...
- Hyperbolic paraboloid (not to be confused with hyperboloid)
- Hyperbolic manifoldHyperbolic manifoldIn mathematics, a hyperbolic n-manifold is a complete Riemannian n-manifold of constant sectional curvature -1.Every complete, connected, simply-connected manifold of constant negative curvature −1 is isometric to the real hyperbolic space Hn. As a result, the universal cover of any closed manifold...
- Hyperbolic spaceHyperbolic spaceIn mathematics, hyperbolic space is a type of non-Euclidean geometry. Whereas spherical geometry has a constant positive curvature, hyperbolic geometry has a negative curvature: every point in hyperbolic space is a saddle point...
- Hyperbolic trajectoryHyperbolic trajectoryIn astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body. Similarly to...