Desigualdades geométricas: fundamentos, problemas e abordagens didáticas no ensino médio

Abstract

This dissertation addresses three classical geometric inequalities—Ptolemaic, Erdös-Mordell, and Isoperimetric—from a historical, theoretical, and pedagogical perspective. Initially, the conceptual foundations and evolution of these inequalities from their origins to their current formulations are presented. Next, applications to mathematical competition problems are analyzed, highlighting their relevance for solving complex problems. Finally, a teaching sequence for high school students is proposed, supported by the use of GeoGebra software and other digital resources, aiming to promote dynamic visualizations and stimulate active learning. The methodology adopted includes a systematic bibliographic review, study of primary sources, and the development of practical activities using digital technologies. The result is a teaching material that integrates mathematical rigor, historical context, and technological resources, contributing to high school mathematics teaching and teacher training by offering innovative strategies for approaching advanced topics in geometry.