Billiard trajectories in the Poincaré disk (hyperbolic geometry). Geodesics are arcs of circles perpendicular to the boundary. Click to set ball direction; watch chaotic reflections.
In hyperbolic geometry (Poincaré disk), geodesics are circular arcs meeting the boundary at right angles. Billiards in hyperbolic tables are chaotic (positive Lyapunov exponent) — nearby trajectories diverge exponentially. Related to Anosov flows and Selberg zeta functions.