Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

This lecture focuses on the geometric properties of surfaces relevant to architecture, particularly the paraboloid and hyperboloid shapes. The instructor begins by discussing the hyperbolic paraboloid, describing it as a ruled surface generated by moving lines along two non-coplanar straight lines in space. The lecture includes practical exercises, demonstrating how to manipulate these surfaces using geometric software. The instructor emphasizes the importance of understanding curvature and developability in architectural design, showcasing various applications of these surfaces in real-world structures. The discussion extends to the implications of curvature in design, including how different shapes can affect structural integrity and aesthetic appeal. The lecture also touches on the mathematical foundations of these surfaces, providing insights into their equations and properties. Throughout the session, the instructor encourages students to visualize and interact with the surfaces, fostering a deeper understanding of their significance in architectural contexts.