Hyperbolic Geometry — Poincaré Disk
Click to place points · geodesics are circular arcs orthogonal to boundary
ds² = 4(dx² + dy²) / (1 − x² − y²)² | K = −1
The Poincaré disk is a model of hyperbolic space with constant curvature K = −1.
Geodesics (shortest paths) are circular arcs meeting the boundary at right angles — or diameters.
Click inside the disk to place two points; their geodesic is drawn. Triangle angles sum to < 180°.