The Poincaré Disk
Nikolai Lobachevsky & János Bolyai, 1830
κ < 0The Poincaré disk is a conformal model of hyperbolic geometry: the entire infinite hyperbolic plane fits inside a circle, with distance expanding toward the boundary. Geodesics are diameters or circular arcs orthogonal to the boundary circle. This exhibit builds a triangle-group tiling by reflection, then traces one geodesic across it.