The Frenet–Serret frame plays a key role in the differential geometry of curves, ultimately leading to a more or less complete classification of smooth curves in Euclidean space up to congruence. The Frenet–Serret formulas show that there is a pair of functions defined on the curve, the torsion and curvature, which are obtained by differentiating the frame, and which describe completely how the frame evolves in time along the curve. A key feature of the general method is that a preferred moving frame, provided it can be found, gives a complete kinematic description of the curve.