Differential Geometry: Surfaces

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Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.

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

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

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

Explores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.

Explores surface and curvature concepts, focusing on TopSolid 7 software and its educational applications.

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.