Comment by Tainnor

You're analogy is flawed. Pythagoras' theorem is about right triangles. "a^2+b^2=c^2" isn't about triangles, it's not even a theorem, it's simply an equation (typically a diophantine one) that is satisfied by some numbers but not others. Something which typically belongs to number theory. Obviously the two things are closely related (which is the beauty of mathematics - there are a lot of connections between very different fields).

But really, I'll refer again to the part of my previous reply where I contextualise why I wrote what I wrote and how that answers the question of whether pi is somehow arbitrary due to the fact that we usually think of space as Euclidean: it's not.