I know that these lumped models are standard in heat transfer calcs, but the application to humans is always interesting. It reminds me a lot of thermal comfort models built to represent human comfort relative to environmental conditions. They all tend to use simplified heat balances to model the heat exchange (with net loss/gain resulting in feeling cold, hot respectively), and there's a couple (Pierce Two-Node Model) which uses two thermal lumps, one for the internal core, and the other for the skin.
Here's my favorite trick: the radians of an angle in a unit circle is equal to the length of the arc of that unit circle.
My interpretation is that I think you guys are missing the fact that the intent of my original comment is in the context approximations, from which you can see the use of the 'trick' is correct.
To break it down a little further: the trick I am referring to is in practice it's often convenient to scale approximations so that you can use the unit circle for calculations, since you can use the radians as a measurement of arc length. If it's not a unit circle, the angle != arc length, so that convenience is lost.
is what I was responding to. My point is this -- there is no derivation happening there. If it was pedantic, obvious and simple to you as you claim, I wonder why you claimed that it was a derivation.
To you the distinction between a definition and a derivation might be a pedantic one, I have doubts on whether that is an universal or even an useful position to have.