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)
|
which has solutions
 |  |  |
(4)
|
 |  |  |
(5)
|
