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hyperbolic line

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  • Hyperbolic triangle — In mathematics, the term hyperbolic triangle has more than one meaning.In the foundations of the hyperbolic functions sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant of the Cartesian plane :{(x,y):x,y in… …   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

  • Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia

  • hyperbolic geometry — Geom. the branch of non Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that two distinct lines may be drawn parallel to a given line through a point not on the given line. Cf. Riemannian geometry …   Universalium

  • Hyperbolic motion — In geometry, a hyperbolic motion is a mapping of a model of hyperbolic geometry that preserves the distance measure in the model. Such a mapping is analogous to congruences of Euclidean geometry which are compositions of rotations and… …   Wikipedia

  • 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-orthogonal — In mathematics, two points in the Cartesian plane are hyperbolically orthogonal if the slopes of their rays from the origin are reciprocal to one another.If the points are ( x , y ) and ( u , v ), then they are hyperbolically orthogonal if : y /… …   Wikipedia

  • hyperbolic geometry — noun (mathematics) a non Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane Karl Gauss pioneered hyperbolic… …   Useful english dictionary

  • hyperbolic — I. adjective also hyperbolical Date: 15th century of, relating to, or marked by hyperbole • hyperbolically adverb II. adjective Date: 1676 1. of, relating to, or being analogous to a hyperbola 2. of, relating to, or being a space in which more… …   New Collegiate Dictionary

  • hyperbolic fix — A fix established by means of hyperbolic lines of position. See hyperbolic position line …   Aviation dictionary

  • hyperbolic position line — Position lines obtained from NAVAIDs (navigational aids) such as CONSOL, LORAN (long range navigation), and DECCA are hyperbolic in shape. These normally are combined with another position line of the same type to obtain a fix. These normally are …   Aviation dictionary

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