Geodesic Curves: Minimizing Distance and Constant Speed

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

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

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

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

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

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

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

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

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

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