Frenet–Serret formulas

Common card · No. 222531

In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space R 3 , {\displaystyle \mathbb {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 available at the time of their discovery. The tangent, normal, and binormal unit vectors, often called T, N, and B, or collectively the Frenet–Serret basis (or TNB basis), together...

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