When Gauss introduced his idea of the spherical image (now called the Gauss map) of a surface, he had to use his imagination and hand drawings to visualize these surfaces. Today, we can use computer graphics to help, and much more is possible now than even 10 years ago. This article revisits a paper originally published in 1982 that illustrates a number of geometric theorems concerning the Gauss map. Unlike its previous version, this one includes many color images and movie clips that demonstrate the transformations described in the text.

• Abstract
• Table of Contents
• Updates (as of 6 July 1998).
• Responses by readers of this article.

• Annotated Bibliography of background and related material.
• Citations that refer to this article.

• Editor's Note

Keywords:

Gauss map, cusp, normal vector, parametric surface

MR Review: 84a:580001
MR Classification: 58C27