Hyperbolic Space — Poincaré Disk
Constant negative curvature K=−1; click to place points and draw geodesics
Click two points to draw a geodesic
In the Poincaré disk model, the entire hyperbolic plane is mapped onto the open unit disk. Geodesics (shortest paths) appear as circular arcs meeting the boundary at right angles (or as diameters). The hyperbolic distance: d(z₁,z₂) = (2/√|K|) arctanh|z₁−z₂|/|1−z̄₁z₂|. The angle sum of any triangle is <π; parallel lines diverge — defect = π − (α+β+γ) = |K|·Area.