Product between angles

In summary, the conversation discusses the concept of multiplying angles and whether there is a geometric interpretation for it. It is mentioned that since angles do not have dimensions, multiplying them is the same as scaling them. The idea of using solid angles or areas of a unit sphere as a way to interpret the product of angles is brought up, but it is noted that this is only an approximation. The conversation ends with the suggestion to use algebra to find the exact correlation between angles and areas.
  • #1
Jhenrique
685
4
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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  • #2
Your question is rather vague.Please Explain it more.
 
  • #3
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
adjacent said:
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:

imagem.jpg


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

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

But exist the solid angles...
 
  • #5
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
I was thinking if the solid angle could have some relationship with the product between plane angles...
 
  • #7
Jhenrique said:
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.)
 
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  • #8
Simon Bridge said:
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...
 
  • #9
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?
 

1. What is the product between two angles?

The product between two angles is the resulting angle when the two angles are multiplied together. This is calculated by multiplying the measures of the two angles in degrees or radians.

2. How do you calculate the product between angles?

To calculate the product between angles, you first need to know the measures of the two angles in degrees or radians. Then, multiply the two measures together and the resulting number will be the product between the angles.

3. Can the product between angles be negative?

Yes, the product between angles can be negative. This occurs when one angle is positive and the other is negative, or when both angles are negative. The resulting angle will be in the fourth quadrant of the coordinate plane.

4. What is the difference between the product between angles and the sum of angles?

The product between angles is the result of multiplying two angles together while the sum of angles is the result of adding two angles together. The product between angles results in a new angle measure, while the sum of angles results in a new angle with a larger measure.

5. In what situations is the product between angles used?

The product between angles is used in trigonometry and geometry to calculate the resulting angle when two angles are multiplied together. It can also be used to find unknown angle measures in geometric figures, such as triangles and quadrilaterals.

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