Intrinsic Geometry of Regular Surfaces

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

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

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

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

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

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

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

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

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