mean curvature (plane curve)

Let Γ be a piecewise C1 planar curve.

The total curvatureMathworldPlanetmathPlanetmath, κtotal , of Γ is defined to be Γ|κ(s)|𝑑s where Γ is parameterized by arclength s and κ(s) is the curvatureMathworldPlanetmathPlanetmath ( of Γ.

The mean curvatureMathworldPlanetmathPlanetmath of Γ is defined to be the ratio of the total curvature to the length of Γ :

Title mean curvature (plane curve)
Canonical name MeanCurvatureplaneCurve
Date of creation 2013-03-22 15:31:16
Last modified on 2013-03-22 15:31:16
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 11
Author Mathprof (13753)
Entry type Definition
Classification msc 53A04
Related topic MeanCurvatureAtSurfacePoint
Defines total curvature
Defines mean curvature