Is there a non-infinitesimal relation between solid angle and plane angles?

[Jhenrique]

Hellow!

I known an infinitesimal relation between the solid angle Ω with the azimutal angle θ and zenital φ, that's given by d²Ω = sin(φ) dφ dθ. But this is infinitesimal relation, exist other relation non infinitesimal between the solind angle with the plane angles? Thanks!

 

[tiny-tim]

Hello Jhenrique!

Solid angle is the same as area (on a unit sphere), for which there are standard formulas.

In particular, if you know all three angles of a triangle, the area is their sum minus π.

(i don't remember the other formulas, but a quick google search will find them )

 

[Jhenrique]

I found nothing more. I thought if an area can have 2 definitions A = xy and dA = dxdy, then the solid angle could have 2 definitions too, 1 algebric definition and 1 infinitesimal definition...