Hyperbolic metric on a punctured disk, showing the cusp that forms at the removed point
This program visualizes the geometrization of a punctured disk: when a point is removed from a disk, the resulting surface admits a complete hyperbolic metric of finite area, in contrast to the flat Euclidean metric of the unpunctured disk. The visualization shows how the hyperbolic metric causes the surface to develop a cusp at the puncture, with geodesics and the metric structure rendered to illustrate this fundamental example from the theory of surfaces and Thurston’s geometrization.
Controls: Click and drag to orbit, scroll to zoom.
