turning number

Noun



 * 1)  A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point.
 * 2) * 2002, Journal of Physics: Mathematical and general, page 6187,
 * For any oriented curve $$\beta(\tau), \tau \in I, I= \left[0, \Lambda\right]$$ of class $$C^1$$ ($$\tau$$ is the arclength parametrization) lying in an oriented Euclidean plane E, the turning number $$\mathcal{T}_{n_\beta}$$ may be defined as
 * $$\mathcal{T}_{n_\beta} = \frac{1}{2\pi}\int_0^\Lambda \kappa_\beta(\tau)d\tau$$
 * where $$\kappa_\beta(\tau)$$ is the signed curvature of β.
 * $$\mathcal{T}_{n_\beta} = \frac{1}{2\pi}\int_0^\Lambda \kappa_\beta(\tau)d\tau$$
 * where $$\kappa_\beta(\tau)$$ is the signed curvature of β.

Usage notes

 * In the animation, the smaller loop that does not go around the origin is also counted.