Curvature and Inflection PointsExplores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Surface of RevolutionExplains the parametric equations of surfaces of revolution generated by curves in space.
Surfaces in GeometryExplores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.
Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Curves in the Oriented PlaneExplores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Envelope of CurvesExplores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.
Differential Geometry: SurfacesExplores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.
