Hyperbolic

Look up hyperbolic in Wiktionary, the free dictionary.

Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.

The following phenomena are described as hyperbolic because they manifest hyperbolas, not because something about them is exaggerated.

• Hyperbolic distribution, a probability distribution characterized by the logarithm of the probability density function being a hyperbola
• Hyperbolic equilibrium point, a fixed point that does not have any center manifolds
• Hyperbolic function, an analog of an ordinary trigonometric or circular function
• Hyperbolic geometry, a non-Euclidean geometry
• Hyperbolic group, a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic geometry
• Hyperbolic growth, growth of a quantity toward a finite-time singularity
• Hyperbolic manifold, a complete Riemannian n-manifold of constant sectional curvature -1
• Hyperbolic navigation, a class of radio navigation systems based on the difference in timing between the reception of two signals, without reference to a common clock
• Hyperbolic number, a synonym for Split-complex number
• Hyperbolic paraboloid, a doubly ruled surface shaped like a saddle
• Hyperbolic partial differential equation, a partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives
• Hyperbolic plane can refer to:
  • The 2 dimensional hyperbolic plane in hyperbolic geometry (a non-Euclidean geometry)
  • The Isotropic quadratic form#hyperbolic plane as isotropic quadratic form
  • The surface of a hyperboloid of one sheet
  • One sheet (usually the positive sheet) of a hyperboloid of two sheets
• Hyperbolic soccerball, a tessellation of the hyperbolic plane
• Hyperbolic space, hyperbolic spatial geometry in which every point is a saddle point
• Hyperbolic trajectory, a Kepler orbit with eccentricity greater than 1
• Hyperbolic geometric graph, a random network generated by connecting nearby points sprinkled in a hyperbolic space

See also

• Exaggeration
• Hyperboloid
• Hyperboloid structure