# Normal, Curvature, Torsion

I don't know if other approaches exist to deriving the Frenet equations, but in my text the curvature is simply defined as the factor that makes $\overrightarrow{T}'(s)$ unit length, and after that the author mentions the geometric interpretation. What I'm saying is that in my text (as well as in a supporting text, actually) we don't have curvature as a geometric "thing" and then discover that the curvature pops out in such-and-such a computation, rather curvature is defined as what popped out and then it's noted that in a particular way this helps describe the curve. My text handles deriving torsion the same way--it plops out of a calculation, and the author notes "since we can't immediately identify it in terms of known quantities, we give it a name". Thus, torsion is defined and, again, not something discovered requiring proof. I dunno, my reasoning in this domain feels impaired but this still seems funky.