Nullhomotopy of a closed curve on $S^2$ and its image under stereographic projection to the plane
Every closed curve on the 2-sphere is nullhomotopic, meaning it can be continuously contracted to a point. This program animates such a nullhomotopy and simultaneously displays its image under stereographic projection onto the plane. As the curve on the sphere shrinks toward the north pole, its stereographic image sweeps out a family of curves that eventually collapses, illustrating the interplay between the topology of the sphere and the conformal geometry of stereographic projection.
Controls: Click and drag to orbit, scroll to zoom.
