What is the unit of omega? I think it does not have a unit because A and r^2 have the same units.
Is A the value of the area on the sphere surface? If so, in practice, how do we calculate its value? Do we do the approximation and assume that A is on a plane?
is A the surface area of a portion of the sphere or is it an approximation onto a plane?
It would be helpful if omega was labeled on the diagram as I'm not sure what quantity it represents.
Why do we measure the ratio of A to r^2 instead of measuring area-to-area ratio?
For sphere, why it's divided by r^2, where does ^2 comes from?
How exactly would you draw the angle that is being calculated? It seems like there can be many regions of area A that would produce different angles?
What exactly does it mean for something to have steradian units? I have no idea what that means since A/r^2 is unitless, meaning we'll need to give it some units, but why not just radians^2 or something like that?
would it be well-defined to have different sum of 2 pi and 4 pi?