EXPLORING PROOFS OF THE PYTHAGOREAN THEOREM

The Pythagorean Theorem has been a cornerstone of mathematics since its discovery, offering profound insights and practical applications across various fields. This paper explores the historical origins and numerous proofs of the theorem, emphasizing its enduring significance. Through an analysis of classical and modern proof techniques, including dissection proofs, similar triangle proofs, and newly discovered frame arrangements, this study highlights the theorem's versatility and impact. Additionally, the paper discusses the wide-ranging applications of the Pythagorean Theorem in contemporary society, from computer graphics and navigation to physics and engineering, demonstrating its essential role in both theoretical and practical contexts.