Parametric Curves: Infinite Branches

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Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Differential Geometry: Curves

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

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Introduces parametric curves and discusses tangent vectors and symmetry properties.

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Explores parametric curves like Lissajous and the Folium of Descartes, discussing tangents, periodicity, and symmetry.

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Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.