# hyperbolic

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## English

### Etymology 1

#### Adjective

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[1]:
At the risk of being slightly hyperbolic, the fourth season of The Simpsons is the greatest thing in the history of the universe.

### Etymology 2

#### Adjective

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 0471610186, page 512 [2]:
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.
• 1998, Katsuhiko Matsuzaki and Masahiko Taniguchi, Hyperbolic Manifolds and Kleinian Groups, 2002 reprint, Oxford, ISBN 0198500629, page 8, proposition 0.10 [3]:
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 0521003504, page 6 [4]:
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 0521003504, page 6 [5]:
Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis ${\displaystyle A_{f}}$ of ${\displaystyle f}$.
##### Translations
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