## Torsion of the curve

a) Prove for each t for which there is a number τ (t) such that . The number τ (t) is called the torsion of the curve at t.
(b) Show that and that a positive value of τ corresponds to the curve twisting toward N.
(c) Verify the validity of the following Fre'net-Serret formulas:

(d) Show that if the curvature is identically zero, then the curve is a straight line
(e) Show that if the torsion is identically zero, then the curve lies in a plane
(f) If the torsion is identically zero and the curvature is a nonzero constant, then show that the curve is a circle.
I already have part (a) answered need help with the others though