Tony, you don't need much theory in this case, 15 is an odd number, the number of magnetpoles must be even for symmetry/balance reasons. Otherwise, somewhere on the ring, you would end up with two neighbouring magnets having the same polarity.
The stator has to have 3,9,12,etc. teeth because we use 3phase controllers. Were we using 5phase controllers, the number of teeth should be a multiple of 5.
