Torsion of curves

In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the plane of curvature. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve. For example, they are coefficients in the system of differential equations for the Frenet frame given by the Frenet–Serret formulas.

Let C be a space curve parametrized by arc length ${\displaystyle s}$ and with the unit tangent vector t. If the curvature ${\displaystyle \kappa }$ of C at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors

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