Hyperbolic functions

Hyperbolic functions
Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster]

2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.'' --Fuller. [1913 Webster]

{Hyperbolic functions} (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called {hyperbolic sines}, {hyperbolic cosines}, etc.

{Hyperbolic logarithm}. See {Logarithm}.

{Hyperbolic spiral} (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • hyperbolic functions — ▪ mathematics also called  hyperbolic trigonometric functions        the hyperbolic sine of z (written sinh z); the hyperbolic cosine of z (cosh z); the hyperbolic tangent of z (tanh z); and the hyperbolic cosecant, secant, and cotangent of z.… …   Universalium

  • Hyperbolic — Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the nature of,… …   The Collaborative International Dictionary of English

  • hyperbolic cosines — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

  • Hyperbolic logarithm — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

  • hyperbolic sines — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

  • Hyperbolic spiral — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… …   The Collaborative International Dictionary of English

  • List of integrals of arc hyperbolic functions — The following is a list of integrals (antiderivative functions) of inverse hyperbolic functions. For a complete list of integral functions, see lists of integrals.: intmathrm{arsinh},frac{x}{c},dx = x,mathrm{arsinh},frac{x}{c} sqrt{x^2+c^2}:… …   Wikipedia

  • List of integrals of hyperbolic functions — The following is a list of integrals (antiderivative functions) of hyperbolic functions. For a complete list of Integral functions, see list of integrals.In all formulas the constant a is assumed to be nonzero, and C denotes the constant of… …   Wikipedia

  • Hyperbolic function — A ray through the origin intercepts the hyperbola in the point , where is twice the area between the ray and the …   Wikipedia

  • Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

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