Cylinders Along Torus Knot: Parametric Curves & Solid Geometry

This GeoGebra demonstration shows how to construct cylinders along a torus knot curve in three-dimensional space. A torus knot is a special type of space curve determined by two coprime integers (p,q), lying on the surface of a torus. Key mathematical concepts include: (1) parametric equations for space curves; (2) computing tangent and normal vectors via derivatives; (3) using vector norms to determine cylinder radius; (4) constructing circular cross-sections perpendicular to the tangent at each point of the curve. Construction details: CurveCartesian command draws the torus knot; Derivative calculates the tangent vector field; Sequence generates points along the curve; norm and vector operations build the cylinder collection. Suitable for advanced mathematics, analytic geometry, or differential geometry courses, demonstrating practical applications of parametric curves, curvature, and Frenet frames.