Isometries in R^2 and R^3

This lecture covers the concept of isometries in R^2 and R^3, including symmetries, rotations, and compositions of linear isometries. The instructor explains how isometries can be generated by rotations and symmetries with respect to lines, emphasizing the preservation of origin. The lecture also touches on the Banach-Tarski paradox and the complexity of isometries in pure math.