ABSTRACT
We assume in general that the direction of the positive i/-axis is given by
a counter-clockwise rotation through an angle — from the direction of the positive x-axis. Definition 7.1. The curvature or signed curvature K of a smooth curve 11-> r(t) at a regular point is the rate of change of direction at that point of the tangent line with respect to arc-length, that is
where arc-length t *-> s(t) is measured along the curve so that s increases as t increases. The absolute curvature of the curve at a point is the absolute value \K\ of the curvature at that point.
