Lecture

Surfaces in Space

Related lectures (31)

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

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

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

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

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

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

Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.

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

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

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

Covers the representation of plane curves and the nature of obtained curves.

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Explores parametric curves, focusing on finding envelopes and caustics.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

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

Explores the Isoclines Method and solutions of differential equations with tangents.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.