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This lecture covers the algebraic resolution of divisions, geometric constructions, Luca Pacioli's contributions, and the constructibility of regular polygons. It explores the relationships between sides, isosceles triangles, and the construction of a pentagon. The lecture delves into the concept of Fermat numbers, their properties, and their significance in geometry. It also discusses the construction of regular polygons, the Gauss-Wantzel theorem, and the limitations of compass and straightedge constructions.