Serpentine curve

A serpentine curve is a curve whose equation is of the form

Equivalently, it has a parametric representation

,

or functional representation

The curve has an inflection point at the origin. It has local extrema at , with a maximum value of and a minimum value of .

HistoryEdit

Serpentine curves were studied by L'Hôpital and Huygens, and named and classified by Newton.

Visual appearanceEdit

 
The serpentine curve for a = b = 1.

External linksEdit