Good point. This should be generalizable to any manifold in any number of dimensions, but I'm most specifically thinking about a line in 2D. For example, K(t)=1/t would be a spiral, but is there a way to derive x(t) and y(t) using K(t), because I've never seen this anywhere.
A year ago I learned in multi-var calc about curvature, and since then I've wondered something. It came up again today when my dad tried to talk to me about curvature like it was the second derivative. :P
Is there a way, or at least any attempt or resource at all, about parameterizing a...