Rhodonea

Curve described in polar coordinates through r = a*sin(n*w). If n is odd the curve has n petals, if n is even it has 2n petals.
The curve is constructed using the script [EUC_Scripts\EUC_Curves\Rhodonea.txt]. In this script the parameters a and n are declared as globals and can be controlled through the data-dialog, appearing by right-clicking on the curve and selecting the [Data] item.

Trifolium

Quadrifolium

The curve defined by the equation f(x,y) = 0, where f(x,y) = (x^2+y^2)^3 - 4*(a*x*y)^2. It is a special [Rhodonea] curve (n=2 in the above polar equation).

Rhodonea with 8 petals (n=4)

Rhodonea with 5 petals (n=5)

Rhodonea with 12 petals (n=6)

Rhodonea with 60 petals (n=30)

http://users.math.uoc.gr/~pamfilos/