M. Schilling catalog # Spindle-shaped surface of constant positive Gaussian curvature

Geodesic lines–Surfaces of revolution of constant Gaussian curvature

The fact that the curvature is constant can be observed by sliding the brass plate presented on the model without its deformations and without losing tight contact with the surface. This brass plate can be continuously (isometrically) deformed into the respectful plate for the sphere. This fact illustrates that the Gaussian curvature is a intrinsic quantity.