Gas-Liquid Interface: Forces, Pressure, and Curvature

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

Geometric Quantities in Parameterized Curves

Explores parameterized curves, regularity, and geometric quantities like the carbide vector and curvature.

Plates II: Föppl-von Kármán Equations

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

Mechanics of Slender Structure: Shells III

Explores the nonlinear theory of spherical shells, including Reissner's solution and Zoelly's solution for pressure buckling.

Mean and Gaussian Curvature

Explores mean and Gaussian curvature, emphasizing their calculation for different bases and surfaces.

Minimal Surfaces: Analytic Examples

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

Altitude Models and Derivative Variables

Covers geographic information systems, relief indicators, and digital elevation models.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Gothic Architecture: Surfaces and Curvature

Delves into the intricate geometry of Gothic architecture, exploring surfaces with variable and constant curvature and the historical evolution of vaults.