Lectures related to Surface of Revolution

Curves in Space: Parametric Equations and Surfaces

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

Surface Integrals: Regular Parametrization

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

Surfaces in Space

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

Closed Surfaces and Integrals

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

Ruled Surfaces: Generators and Applications

Explores ruled surfaces, surfaces generated by moving lines in space, including cones, cylinders, and hyperboloids, with applications in architecture.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

Differential Geometry: Parametric Curves & Surfaces

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

Curvature and Osculating Circle

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

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

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

Curves with Poritsky Property and Liouville Nets

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

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Surfaces in Geometry II

Explores geometric surfaces, rules between shapes, and architectural applications.

Surface Integrals: Implicit Surfaces

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

Perspective of a Sphere & a Circle

Explores conical sections, plane curves, and the perspective of a sphere and a circle.

Regular Curves and Constant Speed

Covers regular curves and constant speed, with examples of circles and helices.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Surfaces with Variable Curvature

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

Conforming Configurations in Veneering: Pseudosphere Example

Covers conforming configurations in veneering, focusing on the pseudosphere example.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Intrinsic Geometry of Regular Surfaces

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