Gaussian Curvature and Geodesics

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

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

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

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

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

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

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

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