# Total Absolute Curvature:

Given a mapping *f *of a surface
*M *into space, the *total absolute curvature* is

where *K * is the Gaussian curvature. It can be shown
that the total absolute curvature is always at least 4 - *X(M)*
where *X(M)* represents the
Euler characteristic of
*M*. When equality holds, the mapping is called
*tight*.

* 8/12/94 dpvc@geom.umn.edu -- *

*The Geometry Center*