Principal Curvatures: Gaussian Curvature

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

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

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

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

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

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

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

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

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

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