Geometric Analysis: Singularities in Architectural Design

This lecture focuses on the geometric analysis of singularities in architectural design, particularly through the study of intersections between geometric forms such as half-cylinders and quarter-spheres. The instructor begins by reviewing previous concepts related to the serpentine line and its regularity, leading into the exploration of stéréotomiques singularities. The lecture emphasizes the importance of understanding the spatial configurations that arise from these intersections, highlighting the role of Frenet frames in analyzing curves in three-dimensional space. The instructor demonstrates how to visualize these interactions and the resulting curves, discussing the implications for architectural design. Various cases are examined, including the tangential connections and the behavior of curves under different orientations. The lecture concludes with a discussion on the significance of curvature and torsion in understanding the geometric properties of surfaces, providing a comprehensive overview of how these concepts apply to architectural forms and their design processes.