Steradian is not independent from radian

[chiphogg]

Very impressive project! 🙂 Nice work.

I noticed that you're treating radians and steradians as separate and completely independent quantities. This isn't right, though; the steradian equals one radian squared. This is easiest to see by considering alternative units for angle and solid angle: the degree, and the square degree (commonly used in astronomy). It happens that the steradian is $(180/\pi)^2$ square degrees, just as the radian is $(180/\pi)$ degrees. And, to complete the argument, the square degree is... well, one degree, squared. 😅