Curvature and Inflection PointsExplores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Differential Geometry: SurfacesExplores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.
Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Gaussian Curvature and GeodesicsExplores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Curves in the Oriented PlaneExplores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Deformation RulesCovers the rules for deforming composite structures and how to trace the deformation based on moment diagrams.
Envelope of CurvesExplores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.
