Re: Radians, dimensions, & explanations

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

I wrote:

> ... because of the radian's unique status, we can always insert the
> radian or any power of the radian into the units of *any* quantity and
> that, similarly, we can remove it from the units of *any* quantity with
> no effect whatsoever on the value of the quantity,

To which Joel responded,

> This is not unique to the *radian*, but would be true of any dimensionless
> unit; would it not?

Joel,

It certainly isn't true for degrees, arcminutes, arcseconds, cycles,
grads, or any other angular unit except the radian, but maybe I just don't
understand what you mean when you refer to a dimensionless unit.  While I
wouldn't be surprised to find other units for which this is true, I don't
think I know of any.  Can you give an example?

John
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