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Cesàro equation

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Title: Cesàro equation  
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Subject: Catenary, Coordinate system, Radius of curvature (applications), Ernesto Cesàro, Evolute, Intrinsic equation, Whewell equation
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Cesàro equation

In geometry, the Cesàro equation of a plane curve is an equation relating the curvature (\kappa) at a point of the curve to the arc length (s) from the start of the curve to the given point. It may also be given as an equation relating the radius of curvature (R) to arc length. (These are equivalent because R = 1/\kappa.) Two congruent curves will have the same Cesàro equation. Cesàro equation's are named after Ernesto Cesàro.

Examples

Some curves have a particularly simple representation by a Cesàro equation. Some examples are:

Related parameterizations

The Cesàro equation of a curve is related to its Whewell equation in the following way, if the Whewell equation is \varphi = f(s)\! then the Cesàro equation is \kappa = f'(s)\!.

References

External links

  • MathWorld.
  • MathWorld.
  • Curvature Curves at 2dcurves.com.
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