This proof assumes that the area a triangle is some function k c^2 of the hypotenuse c where k is constant for similar triangles.
This doesn’t seem super obvious to me, and it’s a bit more than just assuming area scales with the square of hypotenuse length, it indeed needs to be a constant fraction.
To me that truth isn’t necessarily any less fundamental than the Pythagorean theorem itself. But to each their own.
This doesn’t seem super obvious to me, and it’s a bit more than just assuming area scales with the square of hypotenuse length, it indeed needs to be a constant fraction.
To me that truth isn’t necessarily any less fundamental than the Pythagorean theorem itself. But to each their own.
BTW Terrence Tao has a write up of this proof as well: https://terrytao.wordpress.com/2007/09/14/pythagoras-theorem...