An Etymological Dictionary of Astronomy and Astrophysics
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Of or pertaining to a → hyperbola.

From hyperbol-, → hyperbola, + → -ic.

A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (e^x + e^-x).

→ hyperbolic; → cosine.

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.

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.

A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (e^x - e^-x).

→ hyperbolic; → sine.

A three-dimensional space whose geometry resembles that of a saddle-shaped surface and is said to have negative curvature.

→ hyperbolic; → space.