Introduction to DEMR

This lecture introduces the concept of Division in Extreme and Mean Ratio (DEMR), developed by Archytas and Euclide. The DEMR is a mathematical tool used to divide a segment into extreme and mean ratios, with historical connections to the golden ratio. The lecture explains the DEMR's application to segments, its algebraic resolution, and its comparison to simple proportional means. It also covers the fixed values taken by the DEMR and its significance in geometry. The presentation includes practical examples and historical context, highlighting the role of the DEMR in geometric constructions and its divine attributes according to Pacioli's treatise.