Surfaces and Curvature in Geometry

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Related lectures (23)

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Gothic Surfaces: Analysis and Construction

Explores the analysis and construction of Gothic surfaces, focusing on intricate geometrical details and techniques used in architectural design.

Differential Geometry: Parametric Curves & Surfaces

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

Surfaces and Curvature in Geometry

Explores surfaces with variable curvature and the profound impact of curvature sign on geometric properties.

Curvature and Osculating Circle

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

Hyperbolic Geometry

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

Symmetry in Modern Geometry

Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.

Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Shells I: Mechanics of Slender Structures

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

Ellipses and Conics

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Geometry: Course Opening on March 18

Covers course introduction, tutoring, exam dates, and curvature concept.