Hyperbolic Space

We say that spheres are positively curved while hyperbolic space is negatively curved and flat space isn t curved or has curvature 0.

Hyperbolic space. In hyperbolic space in contrast to normal euclidean space euclid s fifth postulate that one and only one line parallel to a given line can pass through a fixed point does not hold. It s sort of like using a map to think about the earth instead of a globe. Wolfram alpha explore anything with the first computational knowledge engine. It is hyperbolic geometry in more than 2 dimensions and is distinguished from euclidean spaces with zero curvature that define the euclidean geometry and elliptic geometry that have a constant positive curvature.

Mathematica the 1 tool for creating demonstrations and anything technical. Hyperbolic space of dimension n is a special case of a riemannian symmetric space of noncompact type as it is isomorphic to the quotient o 1 n o 1 o n. In non euclidean hyperbolic space an infinite number of parallel lines can pass through such read more.