I discovered your website after reading ‘The Man Who Loved Only Numbers’, which mentions Paul Erdős as knowing a good many proofs of the Pythagorean theorem. Can I suggest proof 3 could be derived from a single triangle, dissected into four parts by dropping a perpendicular from halfway along the hypotenuse, and a horizontal from the same point, then halving the rectangle that results?

The areas on the sides of the original triangle would then be 4 times as large as on the small ones derived from it.

Bob Duncan

That's correct. But what's next? The scaled down diagram?