hyperbolic

adj

Etymology: First attested in 1676. By surface analysis, hyperbol(a) + -ic.

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. 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. 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. 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.”