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This lecture explores the evolution of Gothic surfaces in architecture, focusing on the construction techniques used in Gothic cathedrals. It delves into the challenges faced in designing complex surfaces, such as vaults and ogives, and the innovative solutions developed over time. The presentation highlights the unique characteristics of Gothic architecture, including the use of elliptical curves and intricate intersections. The instructor discusses the historical context of Gothic construction, emphasizing the continuous experimentation and refinement of surface design. Through a detailed analysis of key architectural elements, the lecture showcases the ingenuity and engineering prowess of Gothic builders.