W5AIR Mark III Circle Path Mount Hole Reference Model

Why is this useful?
If you design something round and you want to mount it, this model shows how to do it. And, it handles standard hex button head mounting screws.

The model implements the following math formula for determining the number of small circles that can fit on the perimeter of a larger circle.

Question:
Given the diameter of a smaller circle whose origin touches the circumference of a larger circle, how many small circles will fit onto the larger circle?

Answer:
d is Small circle diameter.
D is Large circle diameter.
N is Number of small circles that will fit.
N =(180π^2)/(arcsine(d/D))

How was it implemented in Fusion 360?

N = floor((180π^2)/(arcsine(d/D)) - floor(((180π^2)/(arcsine(d/D)) % 2) - 4

It has a modulo check to ensure the number of holes is even.
I had to put that "-4" in there otherwise all the mounting holes would touch each other's edge.