Division in Extreme and Mean Reason: Luca Pacioli's Influence

This lecture explores the concept of Division in Extreme and Mean Reason (DEMR) as a mathematical tool, tracing its origins from Archytas to Euclid. It delves into the algebraic resolution and geometric construction of DEMR, its applications in constructing regular pentagons, and its relation to Luca Pacioli's work on divine proportions. The lecture also discusses the historical evolution of DEMR's nomenclature and its significance in geometry, including its role in constructing regular polygons and its connection to the concept of the 'golden ratio'.