%0 Journal Article %T The Apple Doesn't Fall Far From the (Metric) Tree: The Equivalence of Definitions %A Asuman G. Aksoy %A Sixian Jin %J Mathematics %D 2013 %I arXiv %X In this paper we prove the equivalence of definitions for metric trees and for \delta-hyperbolic spaces. We point out how these equivalences can be used to understand the geometric and metric properties of \delta-hyperbolic spaces and its relation to CAT(\kappa) spaces. %U http://arxiv.org/abs/1306.6092v1