Newton's method is in fact what is described in the Twitter thread. x → x – f(x)/f'(x) with f = x² – N does in fact give you x → x – [x² – N]/(2 x) Which qui

Newton's method is in fact what is described in the Twitter thread. x → x – f(x)/f'(x) with f = x² – N does in fact give you x → x – [x² – N]/(2 x) Which quickly simplifies to, x → (x + N/x)/2. With that said I am not sure that they knew this coverages quadratically or any of the machinery needed to make Newton's method work... It's a great way to approximate square roots!