# Folium of Descartes

## Description

## 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

## Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive

Patreon me $5. Ask me question on patreon