hyperbolic

• hyperbolick (obsolete)

• Rhymes: -ɒlɪk

hyperbole +‎ -ic

hyperbolic (comparative more hyperbolic, superlative most hyperbolic)

1. Of or relating to hyperbole.
2. Using hyperbole: exaggerated.

   This hyperbolical epitaph. — Fuller.

   • 2012 May 20, Nathan Rabin, “TV: Review: THE SIMPSONS (CLASSIC): “Marge Gets A Job” (season 4, episode 7; originally aired 11/05/1992)”, in The Onion AV Club‎:

     At the risk of being slightly hyperbolic, the fourth season of The Simpsons is the greatest thing in the history of the universe.

hyperbola +‎ -ic

hyperbolic (not comparable)

1. Of or pertaining to a hyperbola.
   • 1988, R. F. Leftwich, "Wide-Band Radiation Thermometers", chapter 7 of, David P. DeWitt and Gene D. Nutter, editors, Theory and Practice of Radiation Thermometry, →ISBN, page 512 :

     In this configuration the on-axis image is produced at the real hyperbolic focus (f_s2) 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.
   • 1998, Katsuhiko Matsuzaki and Masahiko Taniguchi, Hyperbolic Manifolds and Kleinian Groups, 2002 reprint, Oxford, →ISBN, page 8, proposition 0.10 :

     There is a universal constant ${\displaystyle m_{0}>0}$ such that every hyperbolic surface ${\displaystyle R}$ has an embedded hyperbolic disk with radius greater than ${\displaystyle m_{0}}$ .

4. (geometry, topology, of an automorphism) Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.
   • 2001, A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa, and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups, Cambridge, →ISBN, page 6 :

     A hyperbolic isometry ${\displaystyle f}$ has two (distinct) fixed points on ${\displaystyle \partial {\mathcal {H}}}$ .

5. (topology) Of, pertaining to, or in a hyperbolic space (a space having negative curvature or sectional curvature).
   • 2001, A. F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A. F. Costa, and E. Martínez, editors, Topics on Riemann Surfaces and Fuchsian Groups, Cambridge, →ISBN, page 6 :

     Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis ${\displaystyle A_{f}}$ of ${\displaystyle f}$ .