Poincaré Hyperbolic Disk

A 2-D space having Hyperbolic Geometry defined as the 2-Ball $\{x\in\Bbb{R}^2 : \vert x\vert<1\}$, with Hyperbolic Metric

$${dx^2+dy^2\over(1-r^2)^2}.$$

The Poincaré disk is a model for Hyperbolic Geometry, and there is an isomorphism between the Poincaré disk model and the Klein-Beltrami Model.

See also Elliptic Plane, Hyperbolic Geometry, Hyperbolic Metric, Klein-Beltrami Model