Unit Circle Divided in Equal Areas

This diagram constructs a division of a unit circle into n equal areas in a way such that the total sum of the perimeters of the parts is nearly as small as possible. The problem stems from: http://math.stackexchange.com/questions/879940/unit-circle-is-divided-into-n-equal-pieces-what-is-the-least-value-of-the-per
Click on the slider and use arrow keys or drag it with the mouse to change the value of n. It the area pi should be divided into n equal squares their sides would have length sqrt(pi/n). Each band/annulus in the construction has a thickness of approximately this value - rounded to match the nearest multiple of pi/n in the area it encloses.