Lectures related to Developable Surfaces and Parametrization

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

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

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

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

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

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.