Two visualizing proofs of the Pythagorean theorem
This is my first ever blog post. I had some ideas on proving the Pythagorean theorem in a direct and dynamical manner, and recently I find a lot of motivation to write them down and share them on a blog(hopefully I can keep this going), so here we go. I have also written a paper version(the same content as this blog) which can be found at https://vixra.org/abs/2305.0047 . The Pythagorean theorem is one of the most proved theorem of all time, most of the proofs use manipulation of areas to prove that the square of the hypotenuse is indeed the sum of the squares of the two legs. I often felt disconnected with the proofs, it was one of the situations where I could prove something, but could not quite see why. So here let me present two methods of proving the Pythagorean theorem that are hopefully direct, dynamical and visualizing. 1 The question The problem to solve here is quite straight forward: given two side lengths a and b , let them fo...