A WEAK PROOF OF THE PYTHAGOREAN THEOREM

Abstract

Let $C(x, y)$ be the length of the hypotenuse of a right triangle with base length $x$ and height $y$. Then $\{C(x, y)\}^2$ is a quadratic expression of $x, y$. Furthermore, $\{C(x, y)\}^2$ is a symmetric expression of $x$ and $y$. Here, as a restrictive condition, we assume that it is known that the exponents on $x$ and $y$ in the formula of $\{C(x, y)\}^2$ are zero or positive integers. Due to this restrictive condition, only the 6 terms $\left(x^2, y^2, x y, x, y\right.$, and constant term) need to be considered in the formula of $\{C(x, y)\}^2$.

Received: December 3, 2023
Accepted: December 28, 2023