Harmonic Mean: Geometric Projective Geometry

This lecture explores the harmonic mean as a fundamental component of visual arts, allowing the development of the two fundamental invariants of projective geometry: harmonic & anharmonic bi-ratios. It delves into the historical context, from Claude Perrault's architectural contributions to Desargues' perspective division. The lecture also discusses the essential role of harmonic bundles and the invariance properties under various transformations, such as homotheties and projections. The construction of the harmonic mean is demonstrated through ruler and compass constructions, emphasizing its significance in modern projective geometry.