I found this visualizer interesting for looking at the relationship between the solid angle and the radius, and what the area ends up looking like. You could toggle the solid angle to get A=1 with r=1 and get a steradian, and snapshots on the site show solid angles of pi and 2pi
starptr
Interesting to note that at first, it looks like solid angles are fundamentally different from angles (or perhaps liquid angles?) because the subtended area doesn't have a well-defined geometric shape. Our definition even allows for holes and disjoint regions! But actually there is an analogy for angles, which is a set of disjoint arcs, so they're very similar.
rsha256
Steradians appear to be square radians -- why aren't they called squeradians?
I found this visualizer interesting for looking at the relationship between the solid angle and the radius, and what the area ends up looking like. You could toggle the solid angle to get A=1 with r=1 and get a steradian, and snapshots on the site show solid angles of pi and 2pi
Interesting to note that at first, it looks like solid angles are fundamentally different from angles (or perhaps liquid angles?) because the subtended area doesn't have a well-defined geometric shape. Our definition even allows for holes and disjoint regions! But actually there is an analogy for angles, which is a set of disjoint arcs, so they're very similar.
Steradians appear to be square radians -- why aren't they called squeradians?