Serpentine curve - Alchetron, The Free Social Encyclopedia

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

x 2 y + a 2 y − a b x = 0 , a b > 0.

Equivalently, it has a parametric representation

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

or functional representation

y = a b x x 2 + a 2 .

History

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

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