Semicubical parabola

The Neilsche parabola ( after William Neile, who calculated the arc length of this curve for the first time, so-called rectification) or semikubische parable is a special plane curve, or more precisely an algebraic curve of 3rd order.

• Cartesian coordinates equation with a real parameter
• Explicitly:
• Parameter equation:

She is also the evolute of a parabola.

The Neilsche parabola is rational, ie there exists a rational map with an inverse rational mapping that maps the Neilsche parable on the projective line.