Semi-cubic parabola

A third-order algebraic curve in the plane whose equation in Cartesian coordinates is

The origin is a cusp (see Fig.). The length of the arc from the origin equals

and the curvature equals

A semi-cubic parabola is sometimes called a Neil parabola.

Figure: s084040a

References

[1]	A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)
[2]	A.S. Smogorzhevskii, E.S. Stolova, "Handbook of the theory of planar curves of the third order" , Moscow (1961) (In Russian)

References

[a1]	J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
[a2]	F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)