In vector calculus, the Frenet–Serret formulas describe the kinematic properties of a particle which moves along a continuous, differentiable curve in three-dimensional Euclidean space R3. 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 Frederic Frenet, in his thesis of 1847 and Joseph Alfred Serret in 1851. Vector notation and linear algebra currently used to write these formulas was not yet in use at the time of their discovery.

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