Confusing description of torsion of a curve? In my textbook (by do Carmo) and both in wikipedia.
There are descriptions of what a torsion is, and both of them says it is a measure of "how fast a curve twists out of the plane of curvature"
I am aware of the definition of torsion which is the magnitude of the derivative of the binomial vector, but I fail to see how this describes "how fast the curve is twisting out of the plane" or "pulling out of the plane".
If we are talking about how fast the curve is traveling outside of its osculating plane, then this makes absolutely no sense to me at all, since the tangent vector is on the osculating plane.

I'm confused by the relevance of the very last thing you said. The osculating plane is the plane spanned by the tangent vector and the normal vector. The binormal vector is the one pointing out of the plane, so it's derivative represents how fast you twist out of the (osculating) plane.
