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
|Computer-generated tiling of a Poincaré
disk by Jos