Gothic Architecture: Surfaces and Curvature

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Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Curvature and Osculating Circle

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

Vault Intersections

Explores the geometry and types of vault intersections, showcasing historical examples and the generation of vaults, including the architectural marvel of King's College Chapel.

Geometric Principles in Architecture: Hyperboloids and Paraboloids

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.

Hyperboloid Surfaces: Sections and Developability

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

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Surfaces and Curvature in Geometry

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

Surfaces in Geometry

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

Minimal Surfaces: Analytic Examples

Explores minimal surfaces, their properties, history, classification based on curvature, and examples from the Minimal Surfaces Gallery.