hyperbolic

English

Alternative forms

• hyperbolick (obsolete)

Pronunciation

• enPR: hīpərbŏl'ĭk, IPA^(key): /ˌhaɪpɚˈbɑlɪk/
• Rhymes: -ɒlɪk

Etymology 1

hyperbole +‎ -ic

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.

Translations

exaggerated

• Catalan: hiperbòlic
• Czech: nadsazený, nadnesený
• Finnish: hyperbolinen (fi)
• French: hyperbolique (fr) m or f
• German: hyperbolisch, übertrieben (de)
• Irish: áibhéalach, urtheilgeach
• Italian: iperbolico (it)
• (deprecated template usage) {{trans-mid}}
• Manx: ard-vooadagh
• Portuguese: hiperbólico
• Russian: гиперболи́ческий (ru) (giperbolíčeskij), преувели́ченный (ru) (preuvelíčennyj)
• Spanish: hiperbólico (es)
• Swedish: överdriven (sv)

Etymology 2

hyperbola +‎ -ic

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, page 512 [2]:

     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 [3]:

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

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 [4]:

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

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 [5]:

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

Derived terms

• hyperbolic 3-manifold
• hyperbolic algebra
• hyperbolic angle
• hyperbolic automorphism
• 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 orbit
• hyperbolic-orthogonal
• 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

pertaining to a mathematical hyperbola

• Catalan: hiperbòlic
• Czech: hyperbolický
• Danish: hyperbolsk
• Dutch: hyperbolisch (nl)
• French: hyperbolique (fr)
• German: hyperbolisch
• Gujarati: અતિવલયાકાર (ativalyākār)
• (deprecated template usage) {{trans-mid}}
• Icelandic: breiðger m
• Irish: hipearbóileach
• Polish: hiperboliczny
• Portuguese: hiperbólico
• Russian: гиперболический (ru) (giperboličeskij)
• Spanish: hiperbólico (es)
• Swedish: hyperbolisk (sv)