I was kinda kidding about the math part. I don't think many can get by in life without it. At least the basics.
With that pulley in hand, I might have went the way you did. It helps to be able to see what would be left after machining, so may have been too thin. Especially with a servo system.

I have a Tormach lathe and I have been looking for something that may be challenging on it. That looks like a perfect project for it. I have been wanting to try some broaching as well. I will be needing to know how to do that soon enough.