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Division in Extreme and Mean Reason: Euclidean Geometry
This lecture explores the concept of Division in Extreme and Mean Reason (DEMR) as used by Euclid in geometry, focusing on the construction of regular polygons and the historical evolution of the DEMR from a technical tool to a divine proportion. It covers the algebraic resolution of DEMR, geometric constructions, the role of Luca Pacioli, and the significance of DEMR in the construction of the regular pentagon. The lecture delves into the chronology of DEMR's appellations, its relation to the golden ratio, and its applications in establishing metric relationships within polygons.