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.
Gaussian Curvature and GeodesicsExplores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Turbulence: Numerical Flow SimulationExplores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.
Surfaces with Constant CurvatureExplores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.
Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Normal CurvatureExplores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.
