The window "3D Graph" displays the surface X(u,v). The coloring of the surface indicates the sign of the Gaussian curvature in that region. Areas of positive curvature are colored red, areas of negative curvature are colored blue, and areas of zero curvature are colored white. In this example, The torus is divided into two regions, an inner part and an outer part, which correspond to regions of negative and positive Gaussian curvature, respectively.
The window "Gaussian Curvature K(u,v)" visualizes K(u,v) as a function of u and v, defined over the domain of the surface. It is colored in the same manner as the "3D Graph" window.
The demo can be used to look at the sign of the Gaussian curvature for any surface. For example, a sphere, which has constant positive curvature, would be colored completely red, while a plane, which has Gaussian curvature zero, would be colored completely white.