Plot a folium of Descartes with ParametericPlot?

Questions
1

Hi,
Is there anyway to obtain the full plot of Folium of Descartes as parametrized by

x=3t/(1+t^3), 
y=3t^2/(1+t^3)

by ParametricPlot[..] Function in mathematica as there is a discontinuity at t = -1.
Many thanks
JME

2

I don’t see a problem actually:

ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -100, 100}, PlotRange -> 4]

However if you do, depending on the version of Mathematica that you didn’t specify, you could add an explicit Exclusions option. or cut it in to two pieces and combine:

Show[{
 ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -100, -1.01}], 
 ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -0.99, 100}]
 }, 
 PlotRange -> 4
]

Or use a different representation:

ContourPlot[x^3 + y^3 - 3 x y == 0, {x, -3, 3}, {y, -3, 3}]
3

If you give a large enough parameter interval the discontinuity becomes invisible:

folium[t_] = 3 {t, t^2}/(1 + t^3);
ParametricPlot[folium[t], {t, -100, 100}, PlotRange -> 3]