I need to prove that knowing the binormal vector →b(s) of a regular curve α parametrized by arc length is sufficient to know |τ(s)| and κ(s), respectively the module of torsion and the curvature of α.
By the third Frenet Formula, |→b′|=|τ|||→n||=|τ|. No problems here to determine |τ|.
I'm working now in a way to determine κ. What I did was that:
→b=→t∧→n=1κ(→n+τ→b)∧→n=1κ(→n∧→n)+τκ(→b∧→n)=τκ(→b∧→n)
Am I on the right way? What can I do?
