The problem with that definition is that it isn't currently practical, i.e. you can't use it to calibrate machinery.
You can treat radians as a unit or as a ratio, depending on what's convenient. However a significant difference between radians and physical units is that they are defined mathematically rather than based on some experiment.
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branchandroot
Metrology
Date: 2005-04-08 22:11 (UTC)Question: do you count radians as units? Think carefully.
CRB
Re: Metrology
Date: 2005-04-09 17:20 (UTC)You can treat radians as a unit or as a ratio, depending on what's convenient. However a significant difference between radians and physical units is that they are defined mathematically rather than based on some experiment.