Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.
Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.
Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
