Introduction to Euclidean Geometry

This lecture introduces the fundamental concepts of Euclidean geometry, focusing on the postulates and common notions proposed by Euclid. It explores the construction of basic geometric figures using ruler and compass, the concept of parallel lines, and the implications of the fifth postulate. The lecture delves into the distinction between Euclidean and non-Euclidean geometries, discussing the properties of lines on curved surfaces and the absence of parallels in spherical geometry. It also touches upon the development of hyperbolic geometry and the implications of different distance definitions. The presentation concludes with a demonstration of Harriot-Girard's theorem on spherical triangles, showcasing the unique properties of triangles on a sphere.