## Gauss Map

The Gauss map is a function from an Orientable Surface in Euclidean Space to a Sphere. It associates to every point on the surface its oriented Normal Vector. For surfaces in 3-space, the Gauss map of the surface has Degree given by half the Euler Characteristic of the surface

which works only for Orientable Surfaces.

Gray, A. The Local Gauss Map'' and The Gauss Map via Mathematica.'' §10.3 and §15.3 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 193-194 and 310-316, 1993.