Crocheting a Sphere (Math & Program included)

Background

So when crocheting a sphere one does it in rows- essentially making circles stacked on top of each other (rows) with different radii.  To figure out a ‘perfect’ sphere it has to grow and shrink at the same rate as the sin wave.
Here is a video that illustrates the the relation of the circle to the sin wave.
[youtube]http://www.youtube.com/watch?v=Ohp6Okk_tww[/youtube]

Explanation

Each row should scale with sin(theta) where theta is the polar angle (of a sphere).
Goal: to figure out a quadrant of the circle to get the number of crochets for each circle for N, number of rows.
The easiest way to start is to
a.) Figure out the circumference (number of crochets) of the great circle (largest circle in your sphere) . . . This is where sin(theta) = 1 (below: the circle in purple)
b.) Define the number of rows(N) one wants;  N=10 for instance
c.) Since we picked 10 rows, we divide theta for which sin is 1 (90degrees) into 10 parts . . . So sin(90degrees-9degrees) can be used to figure out the radius of the second largest circle and so on.
d.) With each radius (expressed in crochets) you can figure out the circumference (number of crochets the nth largest circle has to have).
Note: When starting chain 2 and proceed with the first row

Play around with the numbers below to see how it all pans out

Program

To figure out # of crochets for half a sphere enter circumference of the sphere (# of crochets) and the number of rows*
[swf src=”http://www.gisellej.com/wp-content/CrochetSphere.swf” width=600 height=400]
*Suggested rows is determined by the circumference of the sphere divided by 2pi, then rounded. This does not hold up for a circumference of less than 30. The smallest size I created was a sphere with a circumference of 6 and 5 rows total (3 rows for the half sphere). It’s still in no way perfect, so suggestions/comments are welcomed :)