Let (x(s), y(s)) be a plane curve parametrized by arclength. Show that the curvature is given by the formula:
C = |x'y'' - x''y'|
The standard formula for curvature is:
where T is the unit tangent vector and equal to:
x'(t) / ||x'(t)||
I don't know where to start here, or even if these are the formulas needed to get to the first equation. Any help would be appreciated!