Serpentine curve

For serpentine shapes in architecture and design, see Serpentine shape.

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

$x^2y+a^2y-abx=0, \quad ab > 0.$

Equivalently, it has a parametric representation

$x=a\cot(t)$, $y=b\sin (t)\cos(t),$

or functional representation

$y=\frac{abx}{x^2+a^2}.$

History

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

Visual appearance

File:Serpentine curve.png

The serpentine curve for a = b = 1.

External links

• MathWorld – Serpentine Equation
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