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I am simulating random angles from 0 to 2π with a uniform distribution. However, if I take the differences between random angles, I get a nonuniform (monotonically decreasing) distribution of angles.
In math speek:
A_{i} = uniform(0,2π)
dA = A_{i}  A_{j}
dA is not uniform.
Here is a rough image of what i'm seeing. P is probability density:
This does not make sense to me. As it seems to imply that the difference between random angles is more likely to be 0 than to be nonzero. You would think it would be uniform, as one angle can be viewed as the *zero* and the other as the random angle. So dA seems like it should also be uniform. What is going on here?
In math speek:
A_{i} = uniform(0,2π)
dA = A_{i}  A_{j}
dA is not uniform.
Here is a rough image of what i'm seeing. P is probability density:
This does not make sense to me. As it seems to imply that the difference between random angles is more likely to be 0 than to be nonzero. You would think it would be uniform, as one angle can be viewed as the *zero* and the other as the random angle. So dA seems like it should also be uniform. What is going on here?
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