By the fact that the geometric proof in the link wants to proof the formula, but only does so for a small subset of all a,b for which the formula is correct. This makes it a partial proof, at best.
Ok nvm I can't resist wasting my time and typing stuff on the internet again, probably gonna regret it later.
How is it not obvious to the dullest of the dull that this visual proof is not supposed to work for goddamn commutative rings lmao
It's probably not even supposed to work for negative reals, 0 or the case b>a. It's supposed to demonstrate the central idea of the visual proof. Also yes, by choosing suitable ways to interpret the lengths shown in the diagrams it's absolutely possible to extend the proof to all reals but I'm not convinced it's meant to be interpreted like that.
But bringing commutative rings into this... man you're funny