Varying b

Even Variation
For this part of our
investigation, we will vary the value of b by even numbers while
keeping a and k constant.
Above we see that our
rose is symmetrical, but we have doubled the number of petals
from k.
This occurs not only
when b is less than k, but also when b is greater than k.
We can see that as
b increases on the even numbers, the rose petals get larger and
larger, yet still stay tight around the origin.
They stay focused on
the origin, because we have not varied a, which we saw to govern
this characteristic earlier.

What if a is larger
than b?
Since we have varied
a, we see the petals spreading from the origin.
But, why is it back
to four petal?
Well, it is just as
the investigation of a went. We now have a larger than b, so we
get the true number of petals to match k.

Odd Variation
For this part of our
investigation, we will vary the value of b by odd numbers while
keeping a and k constant.
Once again, we see
the petal enlargement trend as b increases, with our petals being
double the value of k.
The same thing occurs
when we hold a to be greater than b, as with the even variation.
We have solved another
piece of polar equation puzzle.

Return
to Main Investigation for Conclusions