Let us first look at integer values of k. The following shows the general case when a,b, and k=1.


Now let us look at various integer values for k less than 6.28318530718.









We can see that we seem to be drawing a flower each time, adding one more flower petal or leaf. The value of k gives us the number of petals or leaves. This is called the "nleaf rose".









We can see from the table above that first for different values of a and b, where a<b, gives us two distinct curves. It is an appearance of a flower with two sets of petals. Also notice the difference in the size of the flowers when the values of a and b are changed.









Here we can see that we keep a six petal flower. The only difference is that the flower petals do not intersect at the origin as seen in the previous cases.


