Geometric Transformations: Meanings and Applications

This lecture explores the concept of geometric transformations, focusing on the construction of transformations by varying the factor k, homotheties, and orthogonal projections. It delves into the properties left invariant by different types of transformations, providing a simplified version of the architecture of modern geometry. The lecture also discusses the generation of transformations and the study of properties invariant under homotheties and projections. It concludes with an overview of the relationships between different types of means and their applications in geometry.