serpentine (curve)

The first normal form in Newton's classification of cubic curves was the hardest case:
xy ² + ey = ax ³ + bx ² + cx + d.
The serpentine ¹⁾ curve, serpentine, serpentine cubic or anguinea ²⁾ is a well known subclass of this form.

The curve can be seen as a projection of the horopter.

The serpentine was studied by de L'Hôpital and Huygens (in 1692).
But is was Newton who gave the curve its serpentine name, when he was working on the curve, in 1701.

A generalization of the curve is given by the flipped curve.

notes

1) As having the form of a serpent or snake.

2) Anguis (Lat.) = serpent.
In French: anguinée.