Pipe Helical Surface (Rohrschraubfläche) 3D Demonstration

① This example demonstrates a three-dimensional surface formed by sweeping a circular tube along a helical path, known as a pipe helical surface (Rohrschraubfläche), visually showing how a space curve generates a surface. ② Core mathematical concepts include parametric surfaces, helices (space curves), sweep surfaces, and 3D geometric modeling; it combines the parametric equations of a circle and a helix. ③ Construction highlights: from the construction summary, the GeoGebra commands CurveCartesian and Surface are used to define the helical path and generate the swept surface; objects include radii R and r, parameters p and k, point M, spiral curve, and auxiliary object b, allowing dynamic adjustment of tube thickness and helix pitch. ④ Suitable for high school to undergraduate courses in solid geometry, analytic geometry, or introductory calculus, and for mathematical visualization to help students grasp the intuitive meaning of parametric surfaces and space-curve sweeping.