Equidecomposição no plano e no espaço: do teorema de Wallace-Bolyai-Gerwien ao paradoxo de Banach-Tarski: uma abordagem histórica, conceitual e didática

Abstract

This dissertation investigates the equidecomposition of plane and solid figures and its applications in geometry education, examining theoretical foundations - including the Wallace-Bolyai-Gerwien Theorem for polygons and Hilbert's Third Problem for polyhedra - through to the paradoxical Banach-Tarski result, which challenges intuitive notions of volume. The study culminates in proposing a didactic approach employing geometric dissections and rearrangements to make the learning of areas and volumes more intuitive and meaningful, demonstrating how advanced mathematical concepts can be adapted to enrich basic education through activities that stimulate visualization and spatial reasoning.