View source for Hyperbolic

==English==

===Alternative forms===
* {{l|en|hyperbolical}}
* {{l|en|hyperbolick}} {{qualifier|obsolete}}

===Pronunciation===
* {{enPR|hīpərbŏl'ĭk|a=US}}, {{IPA|en|/ˌhaɪ.pɚˈbɔl.ɪk/}}
* {{audio|en|LL-Q1860 (eng)-Vealhurl-hyperbolic.wav|a=Southern England}}
* {{rhymes|en|ɒlɪk|s=4}}

===Etymology 1===
From {{suffix|en|hyperbole|ic}}.

====Adjective====
{{en-adj}}

# Of or relating to [[hyperbole]].
# Using hyperbole: [[exaggerated]].
#: {{syn|en|exaggerative}}
#* {{quote-journal
|en
|date=May 20, 2012
|author=Nathan Rabin
|title=TV: Review: THE SIMPSONS (CLASSIC): “Marge Gets A Job” (season 4, episode 7; originally aired 11/05/1992)
|work=The Onion AV Club
|url=http://www.avclub.com/articles/marge-gets-a-job,73723/
|page=
|passage=At the risk of being slightly '''hyperbolic''', the fourth season of The Simpsons is the greatest thing in the history of the universe.
}}
# {{lb|en|vision|of a perceived color}} Having a [[saturation]] exceeding 100%.
#: {{hyper|en|chimerical}}
#: {{cot|en|self-luminous|stygian}}
#* {{quote-journal|en|author=Paul Churchland|title=Chimerical colors: some phenomenological predictions from cognitive neuroscience|url=https://www.tandfonline.com/doi/abs/10.1080/09515080500264115?journalCode=cphp20|archiveurl=https://web.archive.org/web/20220616022258/https://www.tandfonline.com/doi/abs/10.1080/09515080500264115?journalCode=cphp20&|archivedate=16 June 2022|accessdate=15 June 2022|journal=Philosophical Psychology|year=2005|volume=18|issue=5|page=553|doi=10.1080/09515080500264115|text=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.}}

=====Translations=====
{{trans-top|exaggerated}}
* Afrikaans: {{t|af|hiperbolies}}
* Catalan: {{t|ca|hiperbòlic}}
* Czech: {{t|cs|nadsazený}}, {{t|cs|nadnesený}}
* Esperanto: {{t|eo|hiperbola}}
* Finnish: {{t+|fi|hyperbolinen}}
* French: {{t+|fr|hyperbolique}}
* Galician: {{t|gl|hiperbólico}}
* German: {{t|de|hyperbolisch}}, {{t+|de|übertrieben}}
* Irish: {{t|ga|áibhéalach}}, {{t|ga|urtheilgeach}}
* Italian: {{t+|it|iperbolico}}
* Manx: {{t|gv|ard-vooadagh}}
* Portuguese: {{t|pt|hiperbólico}}
* Russian: {{t+|ru|гиперболи́ческий}}, {{t+|ru|преувели́ченный}}
* Spanish: {{t+|es|hiperbólico}}
* Swedish: {{t+|sv|överdriven}}
{{trans-bottom}}

===Etymology 2===
{{etymid|en|hyperbola}}
From {{suffix|en|hyperbola|ic}}.

====Adjective====
{{en-adj|-}}

# Of or pertaining to a [[hyperbola]].
#* '''1988''', R.&nbsp;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&nbsp;[http://books.google.com/books?id=SZ6Ldatd7OAC&pg=PA512&dq=hyperbolic]:
#*: In this configuration the on-axis image is produced at the real '''hyperbolic''' focus (f<sub>s2</sub>) but off-axis performance suffers.
# {{non-gloss|Indicates that the specified function is a [[hyperbolic function]] rather than a [[trigonometric function]].}}
#: {{ux|en|The '''hyperbolic''' cosine of zero is one.}}
# {{lb|en|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, [[w:Oxford University Press|Oxford]], {{ISBN|0198500629}}, page 8, proposition 0.10&nbsp;[http://books.google.com/books?id=DLAGEBfEgEUC&pg=PA8&dq=hyperbolic]:
#*: There is a universal constant <math>m_0>0</math> such that every '''hyperbolic''' surface <math>R</math> has an embedded '''hyperbolic''' disk with radius greater than <math>m_0</math>.
# {{lb|en|geometry|topology|of an [[automorphism]]}} Whose [[domain]] has two (possibly [[ideal]]) [[fixed]] [[point]]s [[join]]ed by a [[line]] [[map]]ped to [[itself]] by [[translation]].
#* '''2001''', A.&nbsp;F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A.&nbsp;F. Costa{{,}} and E. Martínez, editors, ''Topics on Riemann Surfaces and Fuchsian Groups'', [[w:Cambridge University Press|Cambridge]], {{ISBN|0521003504}}, page 6&nbsp;[http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic]:
#*: A '''hyperbolic''' isometry <math>f</math> has two (distinct) fixed points on <math>\partial\mathcal H</math>.
# {{lb|en|topology}} Of, pertaining to{{,}} or in a hyperbolic space {{gloss|a space having negative curvature or sectional curvature}}.
#* '''2001''', A.&nbsp;F. Beardon, "The Geometry of Riemann Surfaces", in, E. Bujalance, A.&nbsp;F. Costa{{,}} and E. Martínez, editors, ''Topics on Riemann Surfaces and Fuchsian Groups'', [[w:Cambridge University Press|Cambridge]], {{ISBN|0521003504}}, page 6&nbsp;[http://books.google.com/books?id=RjbQdcP7DgwC&pg=PA6&dq=hyperbolic]:
#*: Exactly one hypercycle is a '''hyperbolic''' geodesic, and this is called the ''axis'' <math>A_f</math> of <math>f</math>.

=====Derived terms=====
{{col3|en
|arc-hyperbolic function|hyperbolic color|nonhyperbolic
|hyperbolic number|inverse hyperbolic function|δ-hyperbolic
|hyperbolic 3-manifold
|hyperbolic algebra
|hyperbolic angle
|hyperbolic automorphism
|hyperbolic colour
|hyperbolic coordinate
|hyperbolic cosecant
|hyperbolic cosine
|hyperbolic cosine integral
|hyperbolic cotangent
|hyperbolic cube
|hyperbolic cylinder
|hyperbolic differential equation
|hyperbolic discounting
|hyperbolic disk
|hyperbolic dodecahedron
|hyperbolic fixed point
|hyperbolic function
|hyperbolic geometry
|hyperbolic group
|hyperbolic growth
|hyperbolic helicoid
|hyperbolic icosahedron
|hyperbolic inverse function
|hyperbolic lemniscate function
|hyperbolic link
|hyperbolic map
|hyperbolic metric
|hyperbolic motion
|hyperbolic navigation system
|hyperbolic octahedron
|hyperbolic-orthogonal
|hyperbolic orbit
|hyperbolic paraboloid
|hyperbolic partial differential equation
|hyperbolic plane
|hyperbolic point
|hyperbolic polar sine
|hyperbolic polyhedron
|hyperbolic polynomial
|hyperbolic quaternion
|hyperbolic rotation
|hyperbolic secant
|hyperbolic secant distribution
|hyperbolic sector
|hyperbolic set
|hyperbolic sine
|hyperbolic sine integral
|hyperbolic small dodecahedral honeycomb
|hyperbolic space
|hyperbolic tangent
|hyperbolic tetrahedron
|hyperbolic time chamber
|hyperbolic trajectory
|hyperbolic triangle
|hyperbolic umbilic catastrophe
|hyperboloid
|quasihyperbolic
|subhyperbolic
|superhyperbolic}}

=====Translations=====
{{trans-top|pertaining to a mathematical hyperbola}}
* Catalan: {{t|ca|hiperbòlic}}
* Czech: {{t|cs|hyperbolický}}
* Danish: {{t|da|hyperbolsk}}
* Dutch: {{t+|nl|hyperbolisch}}
* French: {{t+|fr|hyperbolique}}
* Galician: {{t|gl|hiperbólico}}
* German: {{t|de|hyperbolisch}}
* Gujarati: {{t|gu|અતિવલયાકાર}}
* Hindi: {{t|hi|अतिपरवलयिक}}
* Icelandic: {{t|is|breiðger}}
* Irish: {{t|ga|hipearbóileach}}
* Kazakh: {{t|kk|гиперболалық}}
* Polish: {{t|pl|hiperboliczny}}
* Portuguese: {{t|pt|hiperbólico}}
* Russian: {{t+|ru|гиперболический}}
* Spanish: {{t+|es|hiperbólico}}
* Swedish: {{t+|sv|hyperbolisk}}
{{trans-bottom}}

{{C|en|Hyperbolic functions|Non-Euclidean geometry|Vision}}