Lectures related to Geometric Principles in Architecture: Hyperboloids and Paraboloids

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

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Explores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Explores geometric surfaces, rules between shapes, and architectural applications.

Explores surfaces with constant null curvature and their development, as well as the construction of networks of curves in hyperbolic paraboloids.

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

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

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

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

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

Covers the principles of structural analysis for arches and cables, focusing on geometry and load distribution.

Explores surfaces and curvature in 3D modeling, covering zero curvature, variable curvature, and constant canonical curvatures.

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

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

Covers the key principles of structural design and their implications for architects.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

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

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.