Symmetries in Plane Geometry

This lecture covers the concept of symmetries in plane geometry, focusing on isometries, reflections, and modern symmetry definitions. It explains how symmetries form specific subgroups of isometry groups, both general and particular. The lecture also discusses the definition of symmetries of a figure, the group of symmetries of a figure, and practical applications of symmetries in computer-aided design. The examples include rotations, reflections, and the composition of symmetries in regular polygons. The instructor emphasizes the importance of understanding symmetries for architectural elements like muqarnas. The lecture concludes by highlighting the distinction between intrinsically symmetric objects and mirror images.