Basic:
Compute the curvature of $\langle 2 \cos t^3, 2 \sin t^3, 1 \rangle$.
Intersting:
Consider the curve $C$ parameterized by $\mathbf{r}(t) = \langle t \cos t, t\sin t, t \rangle$.
This curve wraps counterclockwise around the cone $z^2 = x^2 + y^2$. Give an intuitive reason why the curvature
of $C$ should go to zero as the curve winds up the cone. Draw pictures.