December 9th, 2010
In this investigation we look at a polar equation: first there will be a quick introduction followed by some variations of the variables in the equation just to get a feel for what kind of effect they will have on the equation.
Please note: you might need a plugin to play the animations in this page.
2. Our equation
Here is an introduction to polar coordinates and equations:
This is the polar equation we will be working with:
Note what happens when a = b:
Now see what happens if a < b:
And if b < a:
Finally, let's look at different values of k (notice what happens when k is an integer):
Let's keep k constant at 3 so that we three leaves:
Now we do the same with b:
We can also add a value to theta which would have caused a left or right shift in Cartesian coordinates, now has this effect:
Now, by using what we know about the effects of the variables a,b and k, we can create a pretty nice animation (we will keep a = b and increase theta rapidly with some n):
I hope you enjoyed a quick introduction to polar equations.