Chapter 14.4, Problem 86E

To determine

To prove:

There is a number $\tau$(torsion) such that $\frac{dB}{ds}=-\tau N$ using the following steps:

(a) Show that $\frac{dB}{ds}=T\times \frac{dN}{ds}$ and also, conclude that $\frac{dB}{ds}$ is orthogonal to T.

(b) Show that $\frac{dB}{ds}$ is orthogonal to B and also, differentiate $B\cdot B=1$ with respect to s.

(c) Conclude that $\frac{dB}{ds}$ is a multiple of N.