hyperbolic

English

Alternative forms

• hyperbolick (obsolete)

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)”, 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.

Translations

exaggerated

• Catalan: hiperbòlic (ca)
• Finnish: hyperbolinen (fi)
• German: hyperbolisch (de)
• Irish: urtheilgeach (ga)

• Italian: iperbolico (it)
• Manx: ard-vooadagh (gv)
• Spanish: hiperbólico (es)
• Swedish: överdriven (sv)

Etymology 2

hyperbola +‎ -ic

Adjective

hyperbolic (not comparable)

1. Of or pertaining to an 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 [1]:

     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 0198500629, page 8, proposition 0.10 [2]:

     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 0521003504, page 6 [3]:

     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 0521003504, page 6 [4]:

     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-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

pertaining to a mathematical hyperbola

• Catalan: hiperbòlic (ca)
• Czech: hyperbolický (cs) m
• Dutch: hyperbolisch (nl)
• French: hyperbolique (fr)
• German: hyperbolisch (de)

• Icelandic: breiðger (is) m
• Polish: hiperboliczny (pl)
• Spanish: hiperbólico (es)
• Swedish: hyperbolisk (sv)

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.

Translations to be checked

• Czech: nadsazený m, nadnesený m
• French: hyperbolique (fr)

• German: übertrieben (de)