Assignment #11 Polar Equations By Victor L. Brunaud-Vega 1. Investigate   Note: *       When a and b are equal, and  k  is  an       integer, this is one textbook version of       the "n-leaf rose."   *       Compare with   For various k. What if . . . cos( ) is replaced with sin( )? Let us start graphing the first equation   r= a + b * cos (kŻ) It looks like a peach!  But that is not relevant.  But I have no clues, just questions: what is controlled by the parameter a? And b?  What happens if we give several values to k? What happens if we give different values to k?  The picture a right shows the effect, the flower mentioned in class.   What is controlled by the parameter k? This is frustrating.  Let us try keeping b=1 and k=1, and giving different values to a.  I tried a range between -3 and 3, and the result is amazing.  As you can see in the set of pictures below, if a=3 or a=-3, the graph shows a circumference centered in (1,0).   Here is a movie showing the entire sequence.    It looks like a controls the radius of the circumference and probably b controls the center of the circumference. Let us try now keeping a=1 and k=1, and giving different values to b. Here is a movie showing the whole sequence. There is a displacement of the center through the x axis as the value of a changes. Return to EMAT 6680 Page