Isometries & Orientation in Modern Geometry

This lecture covers the fundamental concept of true angle magnitude in space geometry, including the definition of the true angle between two half planes, the sign of the angle, and the rotation direction. It also explores the construction of reflections through inversion, axial reflections, and plane reflections, as well as the generation of isometries through composition of reflections. The lecture delves into the structure theorem of isometries, configurations of two and three planes, and the concept of rotor-reflection. Practical applications in computer-aided design (CAD) are discussed, focusing on reflections in assembly documents and the determination of symmetries in 3D objects.