Hyperbolic

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 angle, an unbounded variable referring to a hyperbola instead of a circle
• Hyperbolic coordinates, location by geometric mean and hyperbolic angle in quadrant I

• 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 geometric graph, a random network generated by connecting nearby points sprinkled in a hyperbolic space
• 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 logarithm, original designation of natural logarithm (1647–1748) before Euler's formulation with e
• Hyperbolic manifold, a complete Riemannian n-manifold of constant sectional curvature −1
• Hyperbolic motion, an isometry in a hyperbolic space
• 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 orthogonality, an orthogonality found in pseudo-Euclidean space
• 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 plane in hyperbolic geometry (a non-Euclidean geometry)
  • The hyperbolic plane as isotropic quadratic form
• Hyperbolic quaternions, a non-associative algebra, precursor to Minkowski space
• Hyperbolic rotation, a synonym for squeeze mapping
• Hyperbolic sector, a planar region demarcated by radial lines and a hyperbola
• 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 versor, a versor parameterized by a hyperbolic angle
• Hyperbolic unit, a non-real quantity with square equal to +1
• Hyperbolic (album), a 2024 album by Pnau

See also

• Exaggeration
• Hyperboloid
• Hyperboloid structure