The Thousand Faces of Pythagoras (As Mil Faces de Pit\'agoras)

TL;DR

This paper explores the Pythagorean Theorem from various perspectives, including its history, applications, generalizations, and lesser-known facets, highlighting its enduring significance and surprising aspects.

Contribution

It offers a comprehensive and unconventional review of the Pythagorean Theorem, revealing new insights and facets often overlooked in traditional treatments.

Findings

Historical overview of the Pythagorean Theorem

Various applications and generalizations discussed

Identification of lesser-known surprising facets

Abstract

The Pythagorean Theorem is one of the oldest, more famous and more useful theorems of Mathematics, and possibly the one that has had the most impact in the evolution of this and other sciences. In this article, we look at it from different perpectives, some of them uncommon. We recall some of its history, some well known applications and generalizations, other less known ones, and show it still has many surprising facets which are usually ignored. (O Teorema de Pit\'agoras (TP) \'e um dos mais antigos, famosos e \'uteis teoremas da Matem\'atica, e possivelmente o que maior impacto teve na evolu\c{c}\~ao desta e outras ci\^encias. Neste artigo, vamos olhar para este velho conhecido de diferentes perspectivas, algumas pouco usuais. Iremos lembrar um pouco da sua hist\'oria, algumas aplica\c{c}\~oes e generaliza\c{c}\~oes bem conhecidas, outras nem tanto, e ver que ele guarda muitas facetas surpreendentes e geralmente ignoradas.)