Now let us see if this works
Now let us see if this works. Can we place two Asquares and two Bsquares into this larger area. That's not hard to do, is it? We can place two of the big Bsquares into the corners, drawn in yellow. As you can see, the two squares overlap the red center. The overlapped area happens to be equal in size to the red square set on the side. With this done, the remaining areas are of the exact size that we need to fit two Asquares into. Thus, the requirement that we set out to achieve, has been achieved with absolute precision.
By following the simple process that Socrates has started, we have discovered a principle of proof that applies to every possible shape of right triangles. And as I promised, no mathematical knowledge was needed to prove to ourselves that what Pythagoras had discovered more than 2,500 years ago is absolutely correct in all possible cases.
