Polar Coordinates

The polar coordinate system is another way of keeping track of points on the plane. Instead of using Descartes' x and y coordinates to determine the position of a point we use r and q. The polar coordinate system is based on a line drawn from the origin of coordinates to the point. The length of this line is r. The angle between the line and the x-axis is q.
The mathematical relationship between cartesian and polar coordinates goes as follows.

x = r cos(q)
y = r sin(q)

The objects cartopol and poltocar convert between cartesian and polar coordinates. The angle is measured in radians. The code is in the comments section.
Lots of very exciting mathematics surrounds this relationship between polar and cartesian coordiantes by way of exponentials and complex numbers. One such jewel is Euler's formula.