Section 13.3: Arc Length & Curvature

Show that the curvature of a plane curve is \(\kappa = |d\phi/ds|\), where \(\phi\) is the angle between \(\mathbf{T}\) and \(\mathbf{i}\); that is, \(\phi\) is the angle of inclination of the tangent line. (This shows that the definition of curvature is consistent with the definition for plane curves given in Exercise 10.2.69.)