nodal curve


last updated: 20031018 
When a is a rational number, the curve is an algebraic
curve.
Each curve consists of equal branches, that merge in a rotation of p/a.
La Gournerie studied the curve in 1851.
Some specific specimen are the following:
For a=1, the kappa curve, a quartic,
results.
For a=2 we see the windmill curve, a sextic
^{1)}.
For a being integer, the power of the curve is 2*a +2.
For a=1/2, you find the straight strophoid.
notes
1) With formula: x^{2}y^{2} (x^{2} + y^{2}) =
(x^{2}  y^{2})^{2}
