A Parabola-like curve with Cartesian equation

(1) |

(2) | |||

(3) |

and Polar Coordinates,

(4) |

The Arc Length, Curvature, and Tangential Angle are

(5) | |||

(6) | |||

(7) |

**References**

Gray, A. ``The Semicubical Parabola.'' §1.7 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 15-16, 1993.

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 85-87, 1972.

Lee, X. ``Semicubic Parabola.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/SemicubicParabola_dir/semicubicParabola.html

MacTutor History of Mathematics Archive. ``Neile's Parabola.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Neiles.html.

Yates, R. C. ``Semi-Cubic Parabola.'' *A Handbook on Curves and Their Properties.* Ann Arbor, MI: J. W. Edwards, pp. 186-187, 1952.

© 1996-9

1999-05-26