Let
$A(r, \theta):=<r\cos \theta, r \sin\theta, \theta>$, $r \in[-1,1], \theta \in [0,2\pi]$ be the parameterization of an area. So this is obviously a helicoid.
(*) Let r be fixed and $\theta$ varying in the interval, then let $\theta$ be fixed and let r vary. what kind of curves would be obtain through this kind of variation? at which angle would they intersect?
So unfortunately I do not have any idea.
I tried to plot it here, https://www.desmos.com/calculator/usy8hfrtbx, for $\theta$ fixed I only got a straight line and for $r$ fixed I got kind of a helix? Can this be right? how could I calculate the angle at which they intersect?
I would be thankful for inputs.
Sometimes a picture is worth 1000 words: