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The following phenomena are described as hyperbolic because they manifest hyperbolas, not because something about them is exaggerated.
- 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 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 space, hyperbolic spatial geometry in which every point is a saddle point
- Hyperbolic trajectory, a Kepler orbit with eccentricity greater than 1
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