Gaussian Curvature and GeodesicsExplores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Differential Geometry: SurfacesExplores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.
Curvature and Inflection PointsExplores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Normal CurvatureExplores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.
Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Surfaces with Constant CurvatureExplores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.
Differential Geometry of SurfacesCovers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.
