> just swap the names
Then you've just skipped the case when a^2 - b^2 is negative. The diagram does not prove that case and swapping the names still doesn't prove it.
Then you've just skipped the case when a^2 - b^2 is negative. The diagram does not prove that case and swapping the names still doesn't prove it.
Not really. If b > a, then swap them to conclude that b^2 - a^2 = (b + a)(b - a), which is what the visual proof demonstrates.
Your conclusion is equivalent to saying that a^2 - b^2 = (a + b)(a - b).
personally, I love visual proofs because they can communicate an idea efficiently, sure they have their pitfalls, but its less about the actual mechanism of the proof and more about the core idea that lets me appreciate how its working- and visual proofs add a pseudo-physical intuition that helps me appreciate it.