Hyperbolic Space
In mathematics, hyperbolic space is a type of non-Euclidean geometry. Whereas spherical geometry has a constant positive curvature, hyperbolic geometry has a negative curvature: every point in hyperbolic space is a saddle point. Parallel lines are not uniquely paired: given a line and a point not on that line, any number of lines can be drawn through the point which are coplanar with the first and do not intersect it. This contrasts with Euclidean geometry, where parallel lines are a unique pair, and spherical geometry, where parallel lines do not exist, as all lines (which are great circles) cross each other. 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.
Read more about Hyperbolic Space: Formal Definition, Models of Hyperbolic Space, Hyperbolic Manifolds
Famous quotes containing the word space:
“Not so many years ago there there was no simpler or more intelligible notion than that of going on a journey. Travel—movement through space—provided the universal metaphor for change.... One of the subtle confusions—perhaps one of the secret terrors—of modern life is that we have lost this refuge. No longer do we move through space as we once did.”
—Daniel J. Boorstin (b. 1914)