Introduction to Euclidean Elements

This lecture introduces the fundamental concepts of Euclidean geometry, including propositions, curves, and the absence of unit measurement. It explores the invariance of distance, the uniqueness of infinity, and alternative geometries like hyperbolic and projective geometry. The lecture covers the surfaces of spheres, hyperboloids, and the Poincaré disk model, as well as the concept of radical axis in circle geometry. It delves into the history of geometry, from Euclid's Elements to modern symmetries and commensurability. The presentation includes practical exercises and the application of geometric principles in architecture and aesthetics.