Assignment 11

Jonathan Beal

"Brrr.....It's Cold in the Polar Equations"

For this investigation, I am going to be torturing some innocent equations that have polar characteristics. I'm not putting any labels on these equations, but they are what they are. They are functions that don't belong here on the regular xy-plane. Oh, no. These are graphed on the r-theta plane. This is a circular plane where r is the length or distance of a point from the center and theta is the angle above the horizontal plane.

Let me examine these equations.

This is an ellipse whose center is x=3 and has a length from the center of 5.

What else is neat about this equation?

My beautiful egg in the previous picture looks smashed open in this picture when n=2

I want to see some other characteristics of this equations on the polar plane.

Some things I noticed:

1. Each equation is centered at the origin.

2. Each arm is 8 away from the center.

3. When n is odd, the odd arm is on the x-axis and the other arms are spread symmetrically from there.

4. When n is even, the figure is symmetrical across 90 degrees and 180 degrees.

As n grows, our egg has hatched a mulit-armed creature that eats lesser armed creatures. It is hard to imagine that my ellipse could grow into this multi-tenacled monster that would be feared by all sea monkeys.