Is There a Geometric Interpretation for the Multiplication or Power of Angles?

[Jhenrique]

Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?

 

[adjacent]

Your question is rather vague.Please Explain it more.

 

[Simon Bridge]

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.

 

[Jhenrique]

Your question is rather vague.Please Explain it more.

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?

Angles don't have any dimensions - so multiplying angles is the same as scaling them.

But exist the solid angles...

 

[Mark44]

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.

 

[Jhenrique]

I was thinking if the solid angle could have some relationship with the product between plane angles...

 

[Simon Bridge]

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.)

 

[Jhenrique]

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?

Yeah! But, I was looking for a exact correlation not approximate...

 

[Simon Bridge]

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?