English: Geodesics (straight lines) are shown on four models of hyperbolic geometry: the upper half-plane, the Poincaré disk model, the pseudosphere and the Klein disk model.

The upper half-plane is parameterized by x horizontally in the range [-30, 30] with divisions every pi/6, and y vertically in the range [0, 40] with divisions every 0.5. These lines are mapped onto the other views.

The red line at y=1 forms the lower boundary of the pseudosphere. The black line at y=0 forms the boundary of the Poincaré and Klein disk models. The orange lines are spaced apart by 2*pi and all map onto the single orange line on the pseudosphere.

The image was produced by the web app at: https://timhutton.github.io/PseudosphereGeodesics/