Folium of Descartes is the curve x^3 + y^3 == 3x*y.
Folium of Descartes is the curve x^3 + y^3 == 3x*y.
This curve is first discussed by Rene Descartes in 1638.
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. folium_descarte.gcf
Polar: r==(3*Sin[θ]*Cos[θ])/(Sin[θ]^3+Cos[θ]^3). folium_descarte_p.gcf
Its asymptote is y==x-1.
A stamp with Descartes and his curve.
See: Websites on Plane Curves, Printed References On Plane Curves.
Robert Yates: Curves and Their Properties.
The MacTutor History of Mathematics archive.