Which concept was first introduced: the pythagoras number of a field or pythagorean fields? I have not found anything on this matter, but my gut feeling says the latter. One can more directly link the idea of pythagorean fields to Pythagoras' theorem, since the equation $c^2 = a^2 + b^2$ has a solution $c$ for any $a, b \in k$ if and only if $k$ is pythagorean. More generally, the concept has geometric implications (see the linked Wikipedia article).
The pythagoras number of a field (or commutative ring), which I'm studying, does not seem directly related to anything Pythagoras did, so my best guess is that the pythagorean fields came first and that the pythagoras number of a field was a generalisation of this. A field is pythagorean if and only if its pythagoras number is one.
Any information (preferably with references) on this you might have is welcome. More broadly, I'd be interested in any information regarding the origin of the term pythagoras number.
