Cosine Spindle Surface: Constructing “Spindelfläche” with Parameters

This example demonstrates how to visualize a cosine-driven spindle surface (Cos-Spindelfläche) and the way its 3D shape varies through parameter choices. The key mathematics includes parametric surface construction, trigonometric functions (especially cosine), continuity and geometric smoothness, and using spherical/circular parameterizations to create a twisted “spindle” structure. Construction highlights: GeoGebra uses Surface to generate the 3D surface, Sequence to iterate parameter values for sampling/animation, and CurveCartesian to define the Cartesian curve data that supports the surface’s shape. The construction involves objects such as Kugel (a spherical reference), Spindel (the main twisted surface), and parameter controls (a, b, n, S1, S2, c, d, e) together with profile elements (profil1, profil2) and buttons (Schaltfläche1, Schaltfläche2) for switching/updating the build. Suitable for high school through early university-level instruction and for interactive exploration of parametric equations and trigonometry in 3D graphing.