I am interested the nodal ($z=0$) behavior of the following functions for a small research project:
$$z=x(x^2-3y^2)$$ $$z=y(3x^2-y^2)$$
When graphed, there are nodes 60° ($n=6$) apart from each other. I am interested in finding analogous equations where there are nodes 72° ($n=5$) apart from each other, where (degrees=$360/n$).
Any help is appreciated. Thank you very much!