Sum of all Spheres https://www.johndcook.com/blog/2019/05/26/sums-of-volumes-of-spheres/ …
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dimensional analysis suggests that this is not a result with any real world application.
You can define some base length scale r_0 and define the ratio r/r_0 = R. Then everything follows just fine.
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Right. Just interpret each term as the volume relative to a unit box. Then every term is dimensionless.
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