EXERCISE 1.63. The unsigned curvature of a plane curve γ(t)-(x(t), v(t)) can be computed with Proposition 1.46 by considering it to have a vanishing third component function: γ(t) (x(t),y(t),0)....
component functions denoted by y(t) ((t), y(t), z(t). The plane curve t) = (x(t), y(t)) represents the projection of γ onto the xy-plane. Assume that γ, is nowhere parallel to (0,0,1), so that γ is regular. Let K and K denote the curvature functions of y and 7 respectively. Let v,v denote the velocity functions of γ and γ respectively. (1) Prove that R 2RV. In particular, at a time t e I for which v(t) lies in the ay-plane,...