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Lecture
Surfaces in Space
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Related lectures (46)
Curves with Poritsky Property and Liouville Nets
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Intrinsic Geometry of Regular Surfaces
Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.
Gaussian Curvature and Geodesics
Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Harmonic Forms: Main Theorem
Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.
Geometric Areas: Integrals and Regions
Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.
Geometrical Aspects of Differential Operators
Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Surface of Revolution
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Explains the parametric equations of surfaces of revolution generated by curves in space.
Closed Surfaces and Integrals
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Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.
Curves in Space: Parametric Equations and Surfaces
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Covers the equations for curves and surfaces in space, including parametric and particular surfaces.
Surface Integrals: Regular Parametrization
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Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.
Differential Geometry: Parametric Curves & Surfaces
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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.
Geometric Surfaces: Paraboloids and Hyperboloids in Architecture
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Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.
Geodesics on Surfaces
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Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.
Dandelin Theorem: Ellipse Construction
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Explores ellipse construction using the Dandelin theorem and properties of conics in space.
Curvature and Osculating Circle
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Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.
Shells I
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Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.
Curves and Surfaces
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Covers the representation of plane curves and the nature of obtained curves.
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