Next week in my multivariable class, we'll be starting curvature, and, nerd that I am, I looked ahead to learn it ahead of time. I can usually at least understand the basics of a new concpet by myself, but curvature really threw me off. Maybe my brain's not right for it, maybe the book sucks, but I know my teacher sucks, so I'm pretty much going to have to learn it myself. I know that curvature is [itex]\kappa=|d\phi/ds|[/itex], where [itex]\phi[/itex] is the angle between the curve's tangent vector and the horizontal, and s is the arc length. I also get that the way to do this is to make it [itex]\kappa=|d\phi/dt/(ds/dt)|[/itex], I get lost, however, in actually finding a good equation for [itex]\phi[/itex]. Does anyone have any tips, resources, or advice?