Summer of Math Exposition

Weirdly enough, with all the proofs of the Pythagoras I had seen, I never felt so connected with them because I wanted something purer and more direct. So one day I decided to try to come up with a proof that could directly show me the raw mechanism, like how does the hypotenuse change with the legs dynamically, without bringing in extra shapes or cleverly manipulating areas. Finally I came up with two proofs that I felt are direct and dynamical in some ways, and hopefully for readers too.