O tratado de Arquimedes sobre esferas e cilindros: uma revisão bibliográfica sobre suas relações de áreas e volumes

Abstract

This study aims to analyze Archimedes' contributions in his treatise On the Sphere and Cylinder, with an emphasis on the relationships between the surfaces and volumes of these solids. The research adopts a historical and bibliographical approach, grounded in the works of Boyer (2012), Contador (2013), Eves (2004), and Garbi (2010) to contextualize the mathematical advancements promoted by Archimedes and their relevance to the development of geometry. The analysis highlights the mathematical proportions presented in the treatise, such as the volume of the sphere being two- thirds of the volume of the circumscribed cylinder, and discusses the application of concepts from Physics. These results underscore the importance of Archimedean thought for classical geometry and its enduring impact on modern mathematics. Finally, the study emphasizes the value of integrating the history of mathematics as a pedagogical tool, offering a more meaningful and contextualized approach to teaching and learning.