Varying k

Even Variation
Let's take a look at
the first case. Here we hae kept a and b constant at 1 and varied
k by even increments.
What do you notice?
We can see that the
number of petals on hte rose has changed as we vary k.
As a matter of fact,
the number of petals corresponds exactly to the value of k.
The petals seem to
be remaining symmetric.

Above we only took
into account if a and b are less than k.
In this next graph
we see if there is any difference if a and b are greater than
k
We still result in
a symmetrical rose with the number of petals equalling k, although
the petals are much larger.

Generalization: When
a and b remain constant, and k is varied evenly, we will get a
symmetric rose with k petals

Odd Variation
Let's see what happens
when a and b remain constant, and k varies by odd numbers.
Our first example keeps
a and b constant at 1.
In the above graph
we can see that the roses do not remain symmetric, however k is
still equal to the number of petals.

If we take into consideration
a and b values larger than k we get
The same thing happens
with the odd values of k as with the even values.

If k is an odd number
and a and b remain constant we will get a rose with k petals,
but it will not be symmetric.

We get the same results
for -k as we did above.
Return
to Main Investigation