# Product between angles

1. Feb 2, 2014

### Jhenrique

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

2. Feb 2, 2014

3. Feb 2, 2014

### 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.

4. Feb 2, 2014

### Jhenrique

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...

5. Feb 2, 2014

### Staff: Mentor

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.

6. Feb 2, 2014

### Jhenrique

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

7. Feb 2, 2014

### Simon Bridge

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.)

Last edited: Feb 2, 2014
8. Feb 3, 2014

### Jhenrique

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

9. Feb 3, 2014

### 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?