Equivalent Sliding Reflection to Three Axial Reflections

This lecture discusses the fundamental theorem on the composition of three axial reflections in a plane, showing that any composition of three arbitrary axial reflections can be expressed as an equivalent sliding reflection. The process involves a translation, two reflections relative to specific lines, and a final axial reflection around an axis. The lecture also covers the notation and conventions used for rotations, reflections, and translations, emphasizing the normalization of the axial reflections into a sliding reflection. The demonstration includes the commutation of reflections and the transformation of the initial axial reflections into a single sliding reflection. The content is illustrated with diagrams and mathematical explanations.