Lectures related to Surfaces in Geometry

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

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

Hyperboloid Surfaces: Sections and Developability

Delves into the properties of hyperboloid surfaces and their sections, emphasizing developability and curvature.

Geometric Principles in Architecture: Hyperboloids and Paraboloids

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.

Surfaces in Geometry II

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

Surfaces and Curvature in Geometry

Explores surfaces, curvature, ruled surfaces, and practical applications in geometry.

Gothic Surfaces: Curvature, Development, and Stereotomy

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Surfaces and Curvature in Geometry

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

Curvature and Osculating Circle

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

Surfaces and Curvature in 3D Modeling

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

Geometric Analysis: Singularities in Architectural Design

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Surfaces with Variable Curvature

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

Dandelin Theorem: Ellipse Construction

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Differential Geometry: Parametric Curves & Surfaces

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

Approximation of Ellipses by Ovals

Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.

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.

Hyperbolic Geometry

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

Surfaces and Curvature in Geometry

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

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Conics in the Plane: Uniform Description of 3 Conics

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.