The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk  [math]\left\{x\in\mathbb{R}:|x|<1\right\}[/math]with hyperbolic metric [math]ds=\frac{dx^2+dy^2}{\left(1-x^2-y^2\right)^2}[/math].  The Poincaré disk is a model for hyperbolic geometry in which a line is represented as an arc of a circle whose ends are perpendicular to the disk’s boundary (and diameters are also permitted). Two arcs which do not meet correspond to parallel rays, arcs which meet orthogonally correspond to perpendicular lines, and arcs which meet on the boundary are a pair of limits rays. [br]

A bit more information can be found at the below link:[br][br]http://mathworld.wolfram.com/PoincareHyperbolicDisk.html