Geometric Transformations: Symmetries and Inversion

This lecture introduces the concept of geometric transformations in the plane, focusing on symmetries and inversion. It covers the definition of geometric transformations, including examples like the identity transformation and constant transformation. The lecture also explains how transformations can turn lines into circles, with a detailed illustration of the inversion effect. Furthermore, it discusses the image of figures under transformations and the importance of the order of vertices in polygons. The concept of isometries, which preserve distances and angles, is explored, emphasizing their role in understanding plane geometry.