expressions for curvature and torsion

For a regularPlanetmathPlanetmathPlanetmath (, parameterized curve α:(a,b)3, not necessarily unit speed, the curvatureMathworldPlanetmathPlanetmath κ(t) and torsion τ(t) are given, respectively, by

κ(t) =α(t)×α′′(t)α(t)3;
τ(t) =(α(t)×α′′(t))α′′′(t)α(t)×α′′(t)2.


John McCleary, GeometryMathworldPlanetmath from a DifferentiableMathworldPlanetmathPlanetmath Viewpoint, Cambridge University Press, 1994.

Title expressions for curvature and torsion
Canonical name ExpressionsForCurvatureAndTorsion
Date of creation 2013-03-22 15:38:14
Last modified on 2013-03-22 15:38:14
Owner Simone (5904)
Last modified by Simone (5904)
Numerical id 7
Author Simone (5904)
Entry type Theorem
Classification msc 53A04
Related topic Torsion
Related topic CurvatureOfACurve