Gothic Architecture: Surfaces and Curvature

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Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Explores the analysis and construction of Gothic surfaces, focusing on intricate geometrical details and techniques used in architectural design.

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Explores surfaces with variable curvature, discussing their construction and properties.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Explores surfaces, curvature, ruled surfaces, and practical applications in geometry.