Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?
As in: ##\theta_1+\theta_2## would mean that an object underwent two rotations ... so what would ##\theta_1\times\theta_2## mean? Angles don't have any dimensions - so multiplying angles is the same as scaling them.
If I had asked what geometrically means the sum of 2 angles, you, probably, show me a draw like: But if I ask what means α×β, what draw you show me for illustrate such product? But exist the solid angles...
I have never come across a situation where angles are multiplied together. To the best of my knowledge there is no reason to do this, so there is no geometric interpretation.
I was thinking if the solid angle could have some relationship with the product between plane angles...
We-ell, by analogy to multiplying two lengths you could argue for an angle-equivalent to an area but I don't know what that would mean. The area of the surface of a unit sphere inside angles ##\theta## and ##\phi## would be (approximately) ##\theta\times\phi## ... that the sort of thing you are thinking of? (Here the angles have to be specially defined.)
Well you could work out the exact version if you like - that's just algebra. How do you find the area of a bit of a sphere?