Solid angle or steradian for measuring

[monty37]

where do we use solid angle or steradian for measuring,in what way
is theuseful over normal angle?

 

[Gear300]

They are useful for proving the generality of Gauss's law for closed surfaces.

 

[Integral]

Consider a sphere and a cone emanating from the center, now how do you apply "normal" angles to describe the cone?

 

[penguin007]

They are also useful in the measure of radiant intensity.

 

[Born2bwire]

Geometric phase problems sometimes has them, like with Foucalt's pendulum.

 

[TheDestroyer]

They are very useful, of course, if you review the definition of Radian, you'll find the it's the angle where the length of the arc is equal to the radius, in different angles, you'll be taking the ratio between the arc and the radius.
In 3D case, you'll find yourself talking about an area and a cone, this cone doesn't necessarily have to be based on a circle, maybe on some elliptical shape, this gives some kind of a generalisation to the definition of an angle in higher dimensions, that it's a ratio, more than being a physical quantity.

If I'm not right, I'd love someone to correct for me :)

Good luck :)

 

[Bob S]

Prove that the surface area of a sphere of radius R is 4 pi R². The 4 pi steradians is the solid angle of the entire surface.

 

[maverick_starstrider]

where do we use solid angle or steradian for measuring,in what way
is theuseful over normal angle?

They're also important in experimental particle scattering where one theoretically calculates the solid body angle.

 

[monty37]

why is it that solid angles are not used while dealing with three dimensional geometry,in mathematics,there all the problems involving cones and spheres were done using normal
angles.