Curves81 of 113
Serpentine curve
Guillaume de l’Hospital and Christiaan Huygens, 1692; Isaac Newton, 1701
Newton named this cubic anguinea, from the Latin for a snake, and classed it in 1701, after L’Hospital and Huygens had studied it in 1692. Its graph y = abx/(x² + a²) climbs from the x axis to a peak of b/2 at x = a, then sinks back toward the axis as x increases. On the other side of the origin it does the same upside down, with its low point of -b/2 at x = -a.
y = abx/(x² + a²)
On mathcurve.com as Anguinée