Identity for Torsion and Radius of Curvature


For a curvewhereis the distance along the curve, ifis the torsion andis the radius of curvature, then


(1) and

Hence(2) whereis the curvature. Differentiating this expression gives

One of the Frenet formulae stateswhereis the binormal vector.

Substituting this expression intogives(3)

Substitute (1), (2) and (3) intoobtaining