Sum-free set

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:

• Line: $\kappa =0$.
• Circle: $\kappa =1/\alpha$, where $\alpha$ is the radius.
• Logarithmic spiral: $\kappa =C/s$, where $C$ is a constant.
• Circle involute: $\kappa =C/{\sqrt {s}}$, where $C$ is a constant.
• Cornu spiral: $\kappa =Cs$, where $C$ is a constant.
• Catenary: $\kappa ={\frac {a}{s^{2}+a^{2}}}$.

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

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

External links

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