Curvature and Oriented Curvature

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Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Covers the concept of line integrals and their application in vector fields.

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Examines geometric singularities in architectural design through the analysis of spatial intersections.

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

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.

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

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