Of or pertaining to a → hyperbola.
Fr.: cosinus hyperbolique
A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (ex + e-x).
→ hyperbolic; → cosine.
Fr.: fonction hyperbolique
Any of the six functions sinh, cosh, tanh, coth, csch, and sech that are related to the → hyperbola in the same way the → trigonometric functions relate to the → circle. Many of the formulae satisfied by the hyperbolic functions are similar to corresponding formulae for the trigonometric functions, except for + and - signs. For example: cosh2x - sinh2x = 1. See also: → hyperbolic cosine, → hyperbolic sine. Hyperbolic functions were first introduced by the Swiss mathematician Johann Heinrich Lambert (1728-1777).
→ hyperbolic; → function.
madâr-e hozluli (#)
Fr.: orbite hyperbolique
An orbit that is an open curve whose ends get wider apart at any rate between that of an ellipse and a straight line. Some comets' orbits become hyperbolic through the gravitational influence of a planet the comet passes near.
→ hyperbolic; → orbit.
Fr.: sinus hyperbolique
A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (ex - e-x).
→ hyperbolic; → sine.
fazâ-ye hozluli (#)
Fr.: espace hyperbolique
A three-dimensional space whose geometry resembles that of a saddle-shaped surface and is said to have negative curvature.
→ hyperbolic; → space.