Torsion of a curve

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Differential geometry

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Explains vector fields, Frenet frame, and local curve behavior using Frenet-Serret formulas.

Tangent Vectors and Bézier Curves

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Curve Parameterization

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Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Curves: Parameterized Curves and Tangent Vectors

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

Arc Length: Circle Circumference and Parametric Curves

Covers circle circumference calculation and parametric curve arc length determination.

Spatial Curves: Singularities and Mechanisms

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Integrals in C: Curvilinear Integration

Explores curvilinear integration in the complex plane, including regular curves, properties, examples, antiderivatives, Cauchy theorem, and integrability criteria.

Geometric Curve Reparameterization

Covers the reparameterization of geometric curves and the concept of 'same geometric curve'.