Trifolium

Cartesian equation: (x+y)(y+x(x+a)) = 4axy

Polar equation: r = a cos (4sin - 1)

Click below to see one of the Associated curves.

Definitions of the Associated curves

Evolute       Involute 1       Involute 2

 Inverse curve wrt origin      Inverse wrt another circle

Pedal curve wrt origin      Pedal wrt another point

Negative pedal curve wrt origin      Negative pedal wrt another point

   Caustic wrt horizontal rays      Caustic curve wrt another point

(x+y)(y+x(x+b)) = 4axy

or, in polar coordinates

r = -b cos + 4a cos sin.

The word 'folium' means 'leaf-shaped'.

There are three special forms of the folium, the simple folium, the double folium and the trifolium. These correspond to the cases

b = 4a, b = 0, b = a

respectively in the formula for the general form.

The graph plotted above is the trifolium. There are separate entries for the simple folium and the double folium.

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