hyperbolic

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English[edit]

Alternative forms[edit]

Etymology 1[edit]

hyperbole +‎ -ic

Adjective[edit]

hyperbolic (comparative more hyperbolic, superlative most hyperbolic)

  1. of or relating to hyperbole
  2. using hyperbole: exaggerated
    This hyperbolical epitaph. — Fuller.
Translations[edit]

Etymology 2[edit]

hyperbola +‎ -ic

Adjective[edit]

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 [1]:
      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 [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[edit]
Translations[edit]
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