Difference between revisions of "Cesàro curve"
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| − | A plane curve whose radius of curvature | + | {{TEX|done}} |
| + | 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|natural equation]] of a Cesàro curve is | ||
| − | + | $$s=\int\frac{dR}{(R/b)^m-1},$$ | |
| − | where | + | where $b$ is a constant and $m$ is a real number. Investigated by E. Cesàro [[#References|[1]]]. |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> E. Cesàro, "Vorlesungen über natürliche Geometrie" , Teubner (1901)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> E. Cesàro, "Vorlesungen über natürliche Geometrie" , Teubner (1901)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)</TD></TR></table> | ||
Latest revision as of 09:01, 3 October 2014
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=22279
Cesàro curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ces%C3%A0ro_curve&oldid=22279
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article