Cartesian equation: (x
+y)(y+x(x+b)) = 4axy
Polar equation: r = -b cos
+ 4a cos sin
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
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 above.
The graph plotted above is the simple folium. There are separate entries for the double folium and the trifolium.
The simple folium is the pedal curve of the tricuspoid where the pedal point is one of the cusps.
Welcome page Famous curves index
Previous curve (Famous curves) Next curve
Biographical Index Chronologies History Topics Index Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions