I'm using Keti Tenenblat's "Introduction to differential geometry" text, and according to the book, we have:
$$T'(s) = K(s)N(s)$$ $$N'(s) = -K(s)T(s) - \tau(s)B(s)$$ $$B'(s) = \tau(s)N(s)$$
where $T(s)$, $N(s)$, $K(s)$, $\tau(s)$ are defined to be, respectively, the tangent vector, the normal vector, the curvature and the torsion and by definition $B(s) = T(s) \times N(s)$.
However, according to wikipedia, the correct formulas would be (and they only agree about $T'(s)$):
$$T'(s) = K(s)N(s)$$ $$N'(s) = -K(s)T(s) + \tau(s)B(s)$$ $$B'(s) = -\tau(s)N(s)$$
What's going on here? I'm trying to solve an exercise about computing the curvature and torsion of the tangent indicatrix that relies on these equations, and it can be found on both hers and O Neil's "Elementary differential geometry" text. However, the former uses the first set of equations and the latter seems to use the second. Wolfram agrees on the second as well.
Already answered in the comments.