Touch the geometry.
Watch the axioms move.
Rotate an elliptic world, construct spherical triangles, and manipulate true hyperbolic geodesics in two equivalent models.
Lab I · Elliptic geometry
A sphere where every line meets.
Great circles are the straight lines of the spherical model. In the elliptic plane, antipodal points are identified, so each pair represents a single point.
Lab II · Hyperbolic geometry
Straight lines that look curved.
Every geodesic is computed as a diameter or a circular arc orthogonal to the disk boundary. Move its defining points and watch the corresponding upper-half-plane geodesic respond.
Objects3 points · 2 geodesics
Latest hyperbolic distance2.016
These pictures preserve mathematical relationships.
The sphere is a model for positive-curvature geometry. The disk and half-plane are two models of the same hyperbolic plane. A curve can represent a straight geodesic because “straight” is defined by the geometry’s metric—not by the appearance of ink on a Euclidean screen.
Read the full explanation →