Δ-hyperbolic space
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- The correct title of this article is δ-hyperbolic space. The initial letter is shown capitalized due to technical restrictions.
In mathematics, a δ-hyperbolic space is a geodesic metric space in which every geodesic triangle is δ-thin.
There are many equivalent definitions of "δ-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 δ 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 δ has to be, the less curved the space is.
The definition of δ-hyperbolic space is generally credited to Eliyahu Rips.
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