If $T$ is the unit tangent vector and $\kappa$ the curvature, is it true that $$\kappa = |T \times \frac{dT}{ds}|$$?
I believe this is true (proof below), but am surprised that I cannot find it anywhere (only the seemingly more complicated formula $\kappa = \frac{|v \times a|}{|v|^3}$).
Proof: $$T' := \frac {dT}{ds} \\ N := \frac {T'} \kappa \\ |T \times N| = 1 \\ |T \times T'| = |T \times \kappa N| = \kappa |T \times N| = \kappa.$$