Geometric Transformations Compositions

This lecture covers the composition of geometric transformations in 2D, focusing on rotations and reflections. The instructor explains how to combine these transformations to achieve specific results, such as billiard problems and mirror reflections. Various examples are provided to illustrate the concepts, including how to calculate the resulting transformation after applying multiple rotations. The lecture also delves into specific cases, such as how to aim a billiard ball to reach a target after a certain number of rebounds. The general results of combining rotations and reflections are highlighted, emphasizing the stability of the resulting transformations. The lecture concludes with practical applications and geometric interpretations of the concepts discussed.