Curvature of Curves and Surfaces { a Parabolic

Parabolas and paraboloids are used to introduce curvature, both qualitatively and quantitatively. 1. Introduction. Most of the standard diierential geometry textbooks recognize the oscu-lating paraboloid as a useful interpretation of the second fundamental form of a surface. This interpretation leads to some qualitative conclusions about the shape of the surface in consideration 9, pp.87,91]. Two extensions are usually ignored: (a) The osculating paraboloid has a planar counterpart, the osculating