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Re: Radians, dimensions, & explanations



A few quibbles, but I basically like what John wrote!

1) show students that the definition of the "radian measure" of an angle
clearly demonstrates that there are, in fact, no units for the radian
measure of an angle,

2) say that we tack on the pseudounit "radian" simply as a courtesy to
people who want to be sure that when we say, properly, "the angle is 1.2"
we are not simply being sloppy and leaving off other possible units for
angle that do not share the radian's unique status,

One can use this, { (1) and (2) above }, as an opportunity to distinguish
between *units* and *physical dimensions*. E.g. *length* is a physical
dimension, the SI unit for length is *meters*. If you make this distinction
then the *radian* is not a psuedo-unit, but is an actual honest-to-gosh
unit; it does happen to be a dimensionless unit!

3) go on to say that, 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,

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

Joel