Torsion of a Curve

High Quality Content by WIKIPEDIA articles! In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve. For example, they are coefficients in the system of differential equations for the Frenet frame given by the Frenet-Serret formulas. Let C be a space curve in a unit-length (or natural) parametrization and with the unit tangent vector t.Let r = r(t) be the parametric equation of a space curve. Assume that this is a regular parametrization and that the curvature of the curve does not vanish.... Mehr