Curves in Space: Parametric Equations and Surfaces

Related lectures (31)

Page 1 of 4

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

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

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

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.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

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

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

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