Poincaré Disk

The disk interior represents the hyperbolic plane; its boundary is not part of it. Geodesics are diameters or circle arcs orthogonal to the boundary. The diagram uses bounded adaptive line approximations, with the same screen scale on both axes.

Calculate once, then examples and valid coordinates update automatically. Drag red vertices to explore. Rejected gestures keep the last valid drawing, including when a sampling limit is exceeded. Background touch and plain wheel scroll normally. Details contains all three coordinate pairs, hyperbolic area and side lengths. Reset triangle restores the symmetric example.

The conformal model preserves angles. Σ is their sum, below180°; δ is the defect,180°−Σ. Tooltips expand these symbols. For curvature K=−1, area equals the defect in radians. Side lengths are hyperbolic distances, not screen distances. Very flat or numerically indistinguishable triangles are rejected; extreme boundary cases may exceed numerical or sampling limits.

SVG exports the current disk and geodesics with resolved colours, labels, model coordinates, angles and measurements in metadata. It is self-contained and does not need this site’s CSS. Only raw coordinates and the selected example are retained, including incomplete inputs. After navigation, calculate again.