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The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh( x / a ) is the catenary , the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.
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.
Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and ...
It is the locus of the center of a hyperbolic spiral rolling (without skidding) on a straight line. It is the involute of the catenary function, which describes a fully flexible, inelastic, homogeneous string attached to two points that is subjected to a gravitational field. The catenary has the equation y(x) = a cosh x / a .
The hyperbolastic rate equation of type II, denoted by H2, is defined as = (() ()),where is the hyperbolic tangent function, is the carrying capacity, and both and > jointly determine the growth rate.
In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles in plane geometry) The use of the hyperbolic functions; The use of gyrotrigonometry in hyperbolic geometry
Pages in category "Hyperbolic functions" The following 25 pages are in this category, out of 25 total. This list may not reflect recent changes. ...
Growth equations. Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects.These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior as input gets large) differs dramatically: