Geodesic Flow in the Poincaré Disk

Hyperbolic geometry: geodesics, ideal triangles, and tessellations in the Poincaré disk model

Mode: geodesics Hyp. dist to center: — Point: —
About: The Poincaré disk models hyperbolic geometry: the entire hyperbolic plane fits inside the unit disk. Geodesics (shortest paths) appear as circular arcs orthogonal to the boundary, or diameters. In hyperbolic geometry, the angle sum of a triangle is less than π, and parallel lines diverge. The hyperbolic distance is d = 2 arctanh(|z|).