Hyperbolic Geometry — Poincaré Disk

Non-Euclidean geometry | Geodesics | Tessellations | ∞ parallel lines

Mode

Click two points to draw a geodesic

Tessellation {p,q}

Hyperbolic Distance

Click two points to measure

About

The Poincaré disk model puts all of hyperbolic space inside the unit disk. Geodesics (straight lines) are circular arcs perpendicular to the boundary. Through any point not on a line, infinitely many parallel geodesics exist — violating Euclid's 5th postulate. Hyperbolic distance: d = 2·arctanh(|z|). The {7,3} tessellation tiles the disk with 0-π heptagons.