View source for Cesàro curve

A plane curve whose radius of curvature <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213501.png" /> at any point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213502.png" /> is proportional to the segment of the normal cut off by the polar (line) of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213503.png" /> with respect to a certain circle. The [[Natural equation|natural equation]] of a Cesàro curve is

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213504.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213505.png" /> is a constant and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c021/c021350/c0213506.png" /> is a real number. Investigated by E. Cesàro [[#References|[1]]].

====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>