Parametric proofs of the Pythagorean theorem via ziggurats and pyramids

TL;DR

This paper introduces two parametric geometric proofs of the Pythagorean theorem using area rearrangement, connecting classical and recent proofs through a unified angular parameter framework.

Contribution

It presents novel parametric constructions that generalize existing proofs of the Pythagorean theorem based on geometric area rearrangements.

Findings

Two new parametric proofs of the Pythagorean theorem

Connection between classical and recent proofs via angular parameters

Proofs depend on simple geometric configurations

Abstract

We propose two new proofs of the Pythagorean theorem via area rearrangement arguments starting from very simple geometric configurations. The constructions depend on an angular parameter, each choice of which yields a proof. For specific values of the parameter, we recover some classical and more recent proofs.