§ Integrating Curvature in 1D [TODO ]
- All curves are parametrized by arc length to avoid weird artefacts by time parametrization.
- So is a function from length of the curve to .
- The (unit?) tangent to a curve is given by .
- The curvature is given by .
- The unit normal is given by .
- We wish to consider the total curvature, given by where is the total length of a closed curve on the plane.
- TODO: how to prove that this will be a multiple of ?