




Assignment #11 Polar Equations 



By Victor L. BrunaudVega 







1. Investigate Note: * When a and b are equal,
and k is an integer, this
is one textbook version of the
"nleaf 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. 












