In this assignment we will examine equations of the form
where a, b, and k values vary.
First let's examine a basic case, a=b=1 and k=3, 4, 5:
So, as we already knew, the case of a=b and k=integer yields the standard n-leaf rose or in this case the k-leaf rose. We see when k=3, we get a 3-leaf rose ( purple). For the case of k=4, we get a 4-leaf rose (red). The case of k=5 yields the 5-leaf rose (green).
Now, I simply want to run through several cases with varying a, b, and k:
Case 1:a<b, k=integer
Case 2: a>b, k= integer
Case 3: k not integer
Case 4: a=0
Case 5: Replace cos( ) with sin ( ):
This concludes our investigation.