I want to create an image in photoshop, and need to break an annulus, pictured below, into smaller segments. I can use other methods to find the solution, but I'm interested to see how mathematicians would handle it.
Here is the image: 
As you can see, there is a grid overlay on the annulus. I would like to know how you would calculate, using this squares on the grid overlay, the number of squares you need to move round in order to create sections of roughly equal size.
Here is what the final output would look like (approximately)
I'm interested in verbose answers as well as formulaic ones