- Hyperbolic Space
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.
