Family of curves
Cartesian coordinates
In an x-y Cartesian coordinate system, the most general form of equation of a siluroid is:
[1]where is a natural integer, that is .
Polar coordinates
Analogously, the most general form of equation of a siluroid in Polar coordinates is:
[2]Parametric formulas
The parametric equations of a siluroid are:
[1a]Mother curve
If we obtain the so called mother curve. Note that the mother curve is a particular case of a more general curve called folium. In particular it is a trifolium where
Cartesian coordinates
In Cartesian coordinates, the mother curve is:
[3]Polar coordinates
In Polar coordinates, the mother curve is:
[4]Solutions
The solutions for the variable y are:
[5]Parametric formulas
The parametric equations of the mother curve are:
[3a]