Let

To study the curvature of S at p, we slice S
by planes containing ** n ** and consider the curvature of the
resulting curves.

**Example:** Let S the graph z=f(x,y) where f(x,y) = x^2-y^2 (the
Saddle) and let p the point (0,0,0).

Slicing the surface with a plane:

Movie showing different resulting curves when we rotate the plane by pi:

The curvatures of these resulting curves are called * normal
curvatures* at **p**.

The maximum normal curvature *k1* and the
minimum normal curvature *k2* are called **principal
curvatures**.

In the movie, k1 is the curvature of the red curve and k2 is the curvature of the blue curve.

Comments to: webmaster@www.geom.uiuc.edu

Created: April 9 1995 ----
Last modified: Sun Apr 28 16:09:52 1996

Copyright © 1995 by
The Geometry Center,
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