Poincaré disk

Poincare disk

Computer-generated tiling of a Poincaré disk by Jos Leys.

The Poincaré disk is the region inside (but not including) a bounding circle, where straight lines are defined to be either diameters of the bounding circle, or arcs of circles that are perpendicular to the bounding circle. The Poincaré disk is a model of hyperbolic geometry. The great flexibility it allows in specifying the angles of a triangle leads to an infinite variety of ways in which the disk can be tiled.