High Quality Content by WIKIPEDIA articles! In mathematics, a ?-hyperbolic space is a geodesic metric space in which every geodesic triangle is ?-thin. There are many equivalent definitions of "?-thin". A simple definition is as follows: pick three points and draw geodesic lines between them to make a geodesic triangle. Then any point on any of the edges of the triangle is within a distance of ? from one of the other two sides. For example, trees are 0-hyperbolic: a geodesic triangle in a tree is just a subtree, so any point on a geodesic triangle is actually on two edges. Normal Euclidean space is ?-hyperbolic; i.e. not hyperbolic. Generally, the higher ? has to be, the less curved the space is.

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