Serpentine curve
A serpentine curve is a curve whose Cartesian equation is of the form
Its functional representation is
Its parametric equation for is
Its parametric equation for is
It has a maximum at and a minimum at, given that
The minimum and maximum points are at, which are independent of.
The inflection points are at, given that
In the parametric representation, its curvature is given by
An alternate parametric representation:
A generalization of the curve is given by the flipped curve when, resulting in the flipped curve equation
which is equivalent to a serpentine curve with the parameters.