A planar curve with curvature radius at an arbitrary point proportional to the length of the segment of the normal MP (see Fig.).
The equation for the Ribaucour curve in Cartesian orthogonal coordinates is
where . If ( is any integer), then a parametric equation for the Ribaucour curve is
The length of an arc of the curve is
and the curvature radius is
This curve was studied by A. Ribaucour in 1880.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|||P.K. Rashevskii, "A course of differential geometry" , Moscow (1956) (In Russian)|
|[a1]||F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)|
Ribaucour curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ribaucour_curve&oldid=36400