Product between angles


by Jhenrique
Tags: angles, product
Jhenrique
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#1
Feb2-14, 03:52 AM
P: 427
Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?
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adjacent
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#2
Feb2-14, 04:15 AM
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Your question is rather vague.Please Explain it more.
Simon Bridge
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#3
Feb2-14, 04:24 AM
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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
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#4
Feb2-14, 02:49 PM
P: 427

Product between angles


Quote Quote by adjacent View Post
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 αβ, what draw you show me for illustrate such product?

Quote Quote by Simon Bridge View Post
Angles don't have any dimensions - so multiplying angles is the same as scaling them.
But exist the solid angles...
Mark44
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#5
Feb2-14, 04:46 PM
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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
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#6
Feb2-14, 04:55 PM
P: 427
I was thinking if the solid angle could have some relationship with the product between plane angles...
Simon Bridge
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#7
Feb2-14, 11:28 PM
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Quote Quote by Jhenrique View Post
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
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#8
Feb3-14, 02:42 AM
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Quote Quote by Simon Bridge View Post
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
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#9
Feb3-14, 04:46 AM
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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?


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