Hilbert curve

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Explores curve parametrization, including setting curves, trace, and direction preservation.

Explains the parametric equations of surfaces of revolution generated by curves in space.

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

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

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

Explores the Richardson cascade, energy cascade, eddy generations, scale separation, Reynolds numbers, and energy contributions.

Covers Bezier curves, de Casteljau Algorithm, properties, derivatives, splines, and end-points.

Explores modeling gene expression, fixed points analysis, and stability in biological systems.

Covers the TNB frame and Frenet-Serret formulas for understanding curve behavior.