Definition of "hyperbolic"

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

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

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.

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

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

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, page 512

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

1998, Katsuhiko Matsuzaki and Masahiko Taniguchi, Hyperbolic Manifolds and Kleinian Groups, 2002 reprint, Oxford, page 8, proposition 0.10

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

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, page 6

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

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, page 6