Regular Polyhedra in Euclidean Geometry

This lecture delves into the historical background of regular polyhedra, exploring their classification, construction, and properties in Euclidean geometry. It covers the work of Isidore de Milet and Anthémius De Tralles, the theory of proportions by Eudoxus, and the inscription of regular polygons in circles. The lecture also discusses the significance of the 5 regular polyhedra inscribed in a sphere, the construction of perfect even numbers, and the proportionality of arcs and angles in circles. It concludes with a recapitulation of the 13 Euclidean species of irrational lines and the geometric configurations introduced by other authors after Euclid.