Cesàro curve

A plane curve whose radius of curvature $R$ at any point $M$ is proportional to the segment of the normal cut off by the polar (line) of $M$ with respect to a certain circle. The natural equation of a Cesàro curve is

$$s=\int\frac{dR}{(R/b)^m-1},$$

where $b$ is a constant and $m$ is a real number. Investigated by E. Cesàro [1].

References

[1]	E. Cesàro, "Vorlesungen über natürliche Geometrie" , Teubner (1901)
[2]	A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)