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Hyperbole (/ h aɪ ˈ p ɜːr b əl i / ⓘ; adj. hyperbolic / ˌ h aɪ p ər ˈ b ɒ l ɪ k / ⓘ) is the use of exaggeration as a rhetorical device or figure of speech. In rhetoric, it is also sometimes known as auxesis (literally 'growth'). In poetry and oratory, it emphasizes, evokes strong feelings, and creates strong impressions. As a ...
Hyperbolic may refer to: of or pertaining to a hyperbola, a type of smooth curve lying in a plane in mathematics Hyperbolic geometry, a non-Euclidean geometry; Hyperbolic functions, analogues of ordinary trigonometric functions, defined using the hyperbola; of or pertaining to hyperbole, the use of exaggeration as a rhetorical device or figure ...
The inverse statement is also true and can be used to define a ... Then the area of the hyperbolic sector is the area of the triangle minus the curved region past ...
The hyperbolic functions take a real argument called a hyperbolic angle. The magnitude of a hyperbolic angle is the area of its hyperbolic sector to xy = 1. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.
This parameter t is the hyperbolic angle, which is the argument of the hyperbolic functions. One finds an early expression of the parametrized unit hyperbola in Elements of Dynamic (1878) by W. K. Clifford .
The curve represents xy = 1. A hyperbolic angle has magnitude equal to the area of the corresponding hyperbolic sector, which is in standard position if a = 1. 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.
The hyperbolic plane is a plane where every point is a saddle point. Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane.
Hyperbolic motions are often taken from inversive geometry: these are mappings composed of reflections in a line or a circle (or in a hyperplane or a hypersphere for hyperbolic spaces of more than two dimensions). To distinguish the hyperbolic motions, a particular line or circle is taken as the absolute.