Product between angles

  1. Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?
     
  2. jcsd
  3. adjacent

    adjacent 1,533
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    Your question is rather vague.Please Explain it more.
     
  4. Simon Bridge

    Simon Bridge 14,649
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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.
     
  5. If I had asked what geometrically means the sum of 2 angles, you, probably, show me a draw like:

    [​IMG]

    But if I ask what means α×β, what draw you show me for illustrate such product?

    But exist the solid angles...
     
  6. Mark44

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

    Simon Bridge 14,649
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    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
  9. Yeah! But, I was looking for a exact correlation not approximate...
     
  10. Simon Bridge

    Simon Bridge 14,649
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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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