Kasey Nored
Polar Equations
We want to explore the following equations
Looking at as we vary a and k we see that changing a only increases the diameter while changing k is interesting
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It appears that when k is even the number of leaves of the rose is equal to 2k and when k is odd the number of leaves equals k.
If we make k negative
The image reflects over the x-axis. The same effect occurs when a is negative, this reflection is masked when k is even due to the symmetry of the image.
When exploring we see that our image is rotated about the center slightly when k is odd.
When k is even the rotation is not discernable.
Looking at if b is even it appears that b just scaled the image.
BUT, if we have an odd b...
a = 1, k = 5, b =1 |
a = 1, k = 5, b =3 |
a = 1, k = 6, b = 1 |
All kinds of things happen... Interestingly, if b = 2 we see the previous images for .
The same types of things happen for
a = 1, k = 6, b =1 |
a =1, k=5, b=1 |
a = 1, k=5, b =3 |
One last equation series...
When c = 1, a =1, k =5 and b = 2 we see...
What a cool way to create a star.
As we vary c our star just gets bigger. Here c = 3 with all other above parameters being the same.
a = 5 the graph shrank |
a = -5 the graph rotated |
b=5 the graph shrank and rotated |
b = -1 the graph rotated |
c = -1 the graph rotated |
k = 4 our graph is really different |
k = 6 same differences as k = 4 |
k = -2 the graph rotates and has the qualities as k = 4 and k =6 |
