4 Jupyter notebooks with SageMath code. Several calculations on curves and surfaces are presented. This includes the computation of many relevant objects associated to curves and surfaces, the verification of important properties in differential geometry and illustrative plots.
There is a notebook with tasks about plane curves, a notebook with computations about space curves and two notebooks about surfaces.
The Jupyter notebooks (.ipynb) include the Markdown cells and the executable SageMath code.
If you want to see the math, plots, interactive elements and code without running it, there are also HTML exports with all the content. They show all the code, explanations, outputs and interactive animations and 3D plots which can be rotated directly from the web browser. Currently, .html files are not rendered directly on GitHub. Therefore, in order to display the full content, download the .html files and open them with your browser.
Some key concepts that appear: Differentiable curve, Regular curve, Parametrization, Length, Trace, Vertex, Evolute, Frenet-Serret trihedron, Tangent vector, Normal vector, Binormal vector, Curvature, Torsion, Osculating plane, Orthogonal projection, First fundamental form, Second fundamental form, Weingarten map, Elliptic point, Hyperbolic point, Parabolic point, Planar point, Principal curvature, Gaussian curvature, Mean curvature, Coordinate curve, Asymptotic curve, Normal curvature, Geodesic curvature, Geodesic.