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.
Gaussian Curvature and GeodesicsExplores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Shells ICovers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.
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 linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.
Curves in the Oriented PlaneExplores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Curves and SurfacesCovers the representation of plane curves and the nature of obtained curves.
Envelope of CurvesExplores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.
