Hyperbolic Geometry: Poincaré Disk Tiling

The hyperbolic plane represented in the unit disk. Geodesics are circular arcs perpendicular to the boundary.

Tiling {p,q}
Depth 3
Rotation θ 0°
Line width 1.0
Negative curvature K=−1. Area of hyperbolic disk of radius r = 4π·sinh²(r/2) — grows exponentially. Regular {p,q} tiling tiles the hyperbolic plane if (p−2)(q−2) > 4. Poincaré disk preserves angles (conformal) but distorts distances: equal-looking triangles are congruent in H².