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Cesàro curve

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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)
How to Cite This Entry:
Cesàro curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ces%C3%A0ro_curve&oldid=33474
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article