I'm still a bit confused by the concept of solid angles. In particular, I don't understand why the region "A" in the diagram is some weird-looking shape. My understanding is that a solid angle is the extension of an angle to three dimensions. If this is the case, wouldn't it make more sense for the region to be a circle? Also, wouldn't it make more sense for a solid angle to be defined by a cone, rather than three line segments as illustrated in the diagram?
@bveeramani For solid angles, the shape doesn't actually matter, only the area. Using a cone is equally valid and most analogous to the radian example above, but isn't required. The three line segment are just a visualization tool to make it clear that we are in 3D.
@tancik I think bveeramani is confused with, since in 2D the angle is precise on shape and position, the reason of chosing a random shape with area A in 3D or higher dimension, which makes it hard to provide an accurate position of that shape. For eample, we have a circle with area A in the same place as the shape in this slide, we will be having a same result. To my understanding bveeramani thinks the "circle" is a better representation of the collection of similar shapes with same area in similar positions, which is also my confusion about solid angles.
The A is just a random cut of the surface. If you had a circle on the surface, that would be representative of the rays from the center being a cone shape. In this case, it just happens to be the oblong shape.