Polar Coordinates and Complex Numbers
PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
We're converting equations from rectangular form to polar form. Here is a slightly harder example. X² plus y² minus the square root of x² plus y², minus y equals 0. So let's recall that x² plus y² is r². So this whole thing can be written as r² minus, and then I have the square root of r² minus, and then y is the same as r sine theta. This is just r.
I have r² minus r minus r sine theta equals 0. Now I can factor r out. I get r minus 1, minus sine theta. That tells me that, in order for this equation to be satisfied, either r equals 0, or r equals 1 plus sine theta.
Now it turns out that r equals 0 is redundant. I don't actually need it. What does r equals 0 represent? Well it represents the point at the origin, the pole. So if I can actually get that point from this equation, I don't need this part.
I do get that point when theta equals 3 pi over 2, because one theta equals 3 pi over 2, this equals-1. So I'll get r equals 0 then. So I don't need this part. This is redundant.
My final equation is just this. So it's actually much simpler in polar coordinates, this equation than in rectangular.