In mathematics, hyperbolic space is a homogeneous space that can be characterized by a constant negative curvature, where in this case the curvature is the sectional curvature. It is the model of hyperbolic geometry. It is possible indimensions 2 or higher, and is distinguished from Euclidean spaces with zerocurvature that define the Euclidean geometry, and models of elliptic geometry that have a constant positive curvature. When embedded to a Euclidean space (of a higher dimension), every point of a hyperbolic space is a saddle point. Another distinctive property is the amount of space covered by the n-ball in hyperbolic n-space: it increases exponentially with respect to the radius of the ball, rather than polynomially.