In
differential geometry, the
Frenet–Serret formulas describe the
kinematic properties of a particle moving along a continuous, differentiable
curve in three-dimensional
Euclidean space R
3, or the geometric properties of the curve itself irrespective of any motion. More specifically, the formulas describe the
derivatives of the so-called
tangent, normal, and binormal unit vectors in terms of each other. The formulas are named after the two French mathematicians who independently discovered them:
Jean Frédéric Frenet, in his thesis of 1847, and
Joseph Alfred Serret in 1851. Vector notation and linear algebra currently used to write these formulas were not yet in use at the time of their discovery.