Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Related lectures (23)

Page 2 of 3

Explores surfaces with variable curvature, discussing their construction and properties.

Explores surfaces with constant null curvature and their development, as well as the construction of networks of curves in hyperbolic paraboloids.

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

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

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

Explores surfaces and curvature in 3D modeling, covering zero curvature, variable curvature, and constant canonical curvatures.

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

Covers the application of the Weingarten map on regular surfaces and the shape operator.

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

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