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Frenet–Serret formulas

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…

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Formulas in n dimensions

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Frenet–Serret formulas

Nodes82
Edges81
Triples36
Avg. degree1.98
Density0.02439
Components1

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Frenet–Serret formulas

Top relations

related to Definitions · 9
Frenet–Serret formulas → Euclidean, In, Let, More, Moreover, Serret, The, The Frenet, Therefore
related to Formulas in n dimensions · 9
Frenet–Serret formulas → Camille Jordan, Euclidean, Frenet, Gram, Schmidt, Serret, Suppose, The, The Frenet
related to Kinematics of the frame · 7
Frenet–Serret formulas → At, Darboux, Hence, Imagine, Serret, The, The Frenet
related to Frenet–Serret formulas in calculus · 5
Frenet–Serret formulas → Explicitly, Note, Serret, The, The Frenet
related to Taylor expansion · 5
Frenet–Serret formulas → For, Frenet, Repeatedly, Serret, Taylor

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Important terminology

curve frenet displaystyle curvature serret torsion mathbf vector frame formulas frac unit normal kappa tangent plane motion binormal along begin

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SubjectPredicateObjectConfidenceSrc
the helixinstance ofSerret formulas are frequently introduced in courses on multivariable calculus as a companion to the study of space curves0.80text
Frenet–Serret formulasrelated to DefinitionsLet0.60section
Frenet–Serret formulasrelated to DefinitionsEuclidean0.60section
Frenet–Serret formulasrelated to DefinitionsThe Frenet0.60section
Frenet–Serret formulasrelated to DefinitionsSerret0.60section
Frenet–Serret formulasrelated to DefinitionsMore0.60section
Frenet–Serret formulasrelated to DefinitionsThe0.60section
Frenet–Serret formulasrelated to DefinitionsIn0.60section
Frenet–Serret formulasrelated to DefinitionsMoreover0.60section
Frenet–Serret formulasrelated to DefinitionsTherefore0.60section
Frenet–Serret formulasrelated to Formulas in n dimensionsThe Frenet0.60section
Frenet–Serret formulasrelated to Formulas in n dimensionsSerret0.60section

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