The following link "disproves" the Pythagorean theorem:

Pythagoras Disproved | Futility Closet

The reason I'm posting it here is because it involves limits, and I have a feeling finding the flaw here is going to involve some analysis. The problem asserts that the red line converges to the hypotenuse, essentially hoping the reader will take this as obvious. I believe that this assertion is false, but I don't know how to actually prove it. Any ideas?