Surfaces with Variable Curvature

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

Explores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

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

Explains the parametric equations of surfaces of revolution generated by curves in space.

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

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

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

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.