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greeno
@Alexnharvey
I think that is because as the number of teeth increase the polygon we're describing more closely approximates to a circle. A circle has a constant ratio of circumference to diameter - pi. Whereas, for the regular decagon of a 10 tooth sprocket, the ratio of the diameter and perimeter is 3.09, for a hexagon it is 3, and the ratio of the diagonal of a square to the perimeter is 2 time square root of 2 or 2.828. The difference between each difference will get smaller and smaller.