Geometric Operations: Inversion & Orthogonal Circles

This lecture covers geometric operations such as inversion relative to a circle, construction of orthogonal circles, and the duplication of the cube. It explores the concept of orthogonality, the significance of radical axes, and the construction of arcs orthogonal to circles. The instructor demonstrates the geometric constructions using both traditional ruler-and-compass methods and modern automated solvers. The lecture delves into the historical context of non-constructible figures, including the quadrature of the circle and the trisection of angles. It also discusses the challenges and solutions in duplicating the cube, emphasizing the importance of cubic roots in ancient geometry.