Definition of "hyperbolic" in English

adjective

1. Of or relating to hyperbole.

2. Using hyperbole: exaggerated.

3. (color theory) Of a perceived color, having a saturation exceeding 100%.

adjective

1. Of or pertaining to a hyperbola.

   • In this configuration the on-axis image is produced at the real hyperbolic focus (fₛ₂) but off-axis performance suffers.

2. Indicates that the specified function is a hyperbolic function rather than a trigonometric function.

   • The hyperbolic cosine of zero is one.

3. (mathematics, of a metric space or a geometry) Having negative curvature or sectional curvature.

   • There is a universal constant m_0>0 such that every hyperbolic surface R has an embedded hyperbolic disk with radius greater than m_0.

4. (geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.

   • A hyperbolic isometry f has two (distinct) fixed points on ∂ℋ.

5. (topology) Of, pertaining to, or in a hyperbolic space (a space having negative curvature or sectional curvature).

   • Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis A_f of f.