01. Polar coordinates, as opposed to Cartesian
Where as a cartesian graph plots coordinates vertically as a function of the horizontal axis (x), a polar graph plots coordinates projecting from the center around which the function rotates (theta).

For example:

sin( x )

1 + cos( x*8 )/8


sin( theta )

1 + cos( theta*8 )/8

Cartesian coordinates are a function of x. As a point rides the x axis, y coordinates returning from the function are plotted on the graph.

Polar coordinates are a function of theta. As theta eternally circles, coordinates indicating the point's distance from the center are plotted on the graph.

Theta is generally calculated in radians: Pi == 180o
A distance of 2Pi will draw a full circle; 360o

Cartesian Polar

f(x) = x

f(theta) = theta
0 <= theta <= 2Pi


0 <= theta <= 2Pi

theta / (8pi)
0 <= theta <= 8Pi

proceed »