hyperbolic

• hyperbolical
• hyperbolick (obsolete)

• (US) enPR: hīpərbŏl'ĭk, IPA^(key): /ˌhaɪ.pɚˈbɔl.ɪk/

• Audio (Southern England):

  (file)

• Rhymes: -ɒlɪk

From hyperbole +‎ -ic.

hyperbolic (comparative more hyperbolic, superlative most hyperbolic)

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

   Synonym: exaggerative

   • 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.

3. (vision, of a perceived color) Having a saturation exceeding 100%.

   Hypernym: chimerical

   Coordinate terms: self-luminous, stygian

   • 2005, Paul Churchland, “Chimerical colors: some phenomenological predictions from cognitive neuroscience”, in Philosophical Psychology‎, volume 18, number 5, →DOI, archived from the original on 16 June 2022, page 553:

     Using the techniques already explored, we can contrive to activate a coding triplet in any one of those four extremal corners. If one fixates at length on a pale blue-green stimulus, as in Figure 18, and then refixates on an already maximally saturated orange surface, then the resituated f/p vector will yield an activation triplet within the farthest corner of the cube, beyond the limits of the classical spindle. The H–J theory of our internal color representations entails that one should there find a circular after-image of a hyperbolic orange, an orange that is more "ostentatiously orange" than any (non-self-luminous) orange you have ever seen, or ever will see, as the objective color of a physical object. Row 1 of Figure 19 will allow you, once more, to test such a prediction for yourself.

From 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 ${\displaystyle f}$.