Surfaces with Constant Curvature

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Geometric Surfaces: Paraboloid and Hyperboloid Concepts

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

Gothic Architecture: Surfaces and Curvature

Delves into the intricate geometry of Gothic architecture, exploring surfaces with variable and constant curvature and the historical evolution of vaults.

Approximation of Ellipses by Ovals

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

Hyperbolic Geometry

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

Surfaces in Geometry II

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

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.

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Spatial Curves: Singularities and Mechanisms

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Surfaces: Curvature and Development

Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.