The Maximum and Minimum of the Normal Curvature and at a given point on a
surface are called the principal curvatures. The principal curvatures measure the Maximum and Minimum
bending of a Regular Surface at each point. The Gaussian Curvature and Mean Curvature
are related to and by

(1) | |||

(2) |

This can be written as a Quadratic Equation

(3) |

(4) | |||

(5) |

**References**

Geometry Center. ``Principal Curvatures.'' http://www.geom.umn.edu/zoo/diffgeom/surfspace/concepts/curvatures/prin-curv.html.

Gray, A. ``Normal Curvature.'' §14.2 in *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 270-273, 277, and 283, 1993.

© 1996-9

1999-05-26