Folium of Descartes

foliumOfDescartes.nb.zip.

Description

folium of Descartes
Folium of Descartes is the curve x^3 + y^3 == 3x*y.

History

This curve is first discussed by Rene Descartes in 1638.

Formula

Cartesian: x^3 + y^3 == 3x*y.

Parametric: {3*t, 3t^2}/(1 + t^3). In this formula, the curve tends to the Origin as t→±∞. The curve tends to ∞ when t→-1.

Polar: r==(3*Sin[θ]*Cos[θ])/(Sin[θ]^3+Cos[θ]^3).

Its asymptote is y==x-1.

Properties

descartes stamp
A stamp with Descartes and his curve.

Related Web Sites

See: Websites on Plane Curves, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive