The Frenet-Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion. They give the derivatives of the tangent, normal and binormal unit vectors, called T, N and B, in terms of each other: along the arclength, the derivative of T is the curvature times N, the derivative of N is minus the curvature times T plus the torsion times B, and the derivative of B is minus the torsion times N. Curvature measures how far a curve is from being a straight line, and torsion measures how far it is from being planar. The formulas are named after two French mathematicians who discovered them independently, Jean Frédéric Frenet in his thesis of 1847 and Joseph Alfred Serret in 1851, before the vector notation and linear algebra used to write them today were available. The three vectors form an orthonormal basis, the Frenet-Serret frame, which moves along the curve, and the frame is used in physics, for example in relativity theory, and in models of microbial motion.
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Source Frenet-Serret formulas (Wikipedia)
Source Frenet-Serret formulas (Wikipedia)
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Source Frenet-Serret formulas (Wikipedia)Applications and interpretation, ApplicationsQuote, Applications and interpretation, Applications
Such is often the case, for instance, in relativity theory.
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1. MacTutor History of Mathematics: Jean Frédéric Frenet (MacTutor)
MacTutor History of MathematicsBiography, thesisQuote, Biography, thesis
he wrote a doctoral thesis there which he submitted in 1847
Frenet-Serret formulas (Wikipedia)
Applications and interpretation, Applications
Such is often the case, for instance, in relativity theory.
In Branch: Differential Geometry, Lead
In differential geometry, the Frenet-Serret formulas describe the kinematic properties
In Group: Differential Geometry, Lead, topic area
In differential geometry, the Frenet-Serret formulas describe the kinematic properties
Proved By: Jean Frédéric Frenet, Lead, discoverers
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.
Proved By: Joseph Alfred Serret, Lead, discoverers (Serret)
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.
Named After: Jean Frédéric Frenet, Lead, eponyms
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.
Named After: Joseph Alfred Serret, Lead, eponyms (Serret)
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.
Has Statement Form: Equation, Lead, formulas
The Frenet-Serret formulas are:
Principal Result Of: Joseph Alfred Serret, Lead, discoverers (Serret)
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.
View the SourceJean Frédéric Frenet (Wikipedia)
Principal Result Of: Jean Frédéric Frenet, Lead, best knownQuote, Principal Result Of: Jean Frédéric Frenet, Lead, best known
He is best known for being an independent co-discoverer of the Frenet-Serret formulas.
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