Definition:Torsion of Curve Parameterized by Arc Length/3-Dimensional Real Vector Space

Definition
Let $\alpha : I \to \R^3$ be a (smooth) curve parameterized by arc length.

Let $s \in I$ be such that the curvature $\map \kappa s \ne 0$.

The torsion of $\alpha$ at $s$ is the real number $\map \tau s$ defined by:
 * $\map {b'} s = \map \tau s \map n s$

where:
 * $\map {b'} s$ is the derivative of the binormal vector
 * $\map n s$ is the normal vector

Also see

 * Torsion of Curve Parameterized by Arc Length is Well-Defined