The property of being hyperbolic.

(uncountable) The use of hyperbole / (countable) An instance of hyperbole / (countable, geometry) A blow-up of a curve at a point.

simple past tense and past participle of hyperbolize

Third-person singular simple present indicative form of hyperbolize

(mathematics) A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t.

(mathematics) A hyperbolic function that is the analogue of the sine function for hyperbolic spaces, taking in a hyperbolic angle as an argument and returning the y-coordinate for the corresponding point on the unit hyperbola. It is written in symbol sinh and can be represented as: sinh (x)= tfrac 1 2(eˣ-e⁻ˣ)

(mathematics) a hyperbolic function that is written in symbol tanh and defined as the following:

(mathematics) a hyperbolic function that is written in symbol cosh and defined as the following: cosh (x)= tfrac 1 2(eˣ+e⁻ˣ)

(mathematics) A set functions that are analogues of the trigonometric functions for hyperbolic spaces. They can be derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.

(mathematics) Any space exhibiting hyperbolic geometry rather than Cartesian geometry