Spherical Coordinates – Sweeping Out a Sphere

① This example dynamically demonstrates how a complete sphere can be generated by sweeping out a surface using spherical coordinates (radial distance r, polar angle ψ, and azimuthal angle φ). ② Core mathematical concepts include the spherical coordinate system, parametric surfaces, the equation of a sphere, meridians and parallels, and rotational sweeping in 3D space. ③ Construction highlights: using GeoGebra commands such as Sphere, IntersectPath, Segment, CircleSector, Plane, and Surface; objects include sliders r, fi, psii, auxiliary points A, Axy, Ax, and multiple buttons (przycisk1–7) to control the sweeping animation. ④ Suitable for senior high school or early university students learning multivariable calculus, solid geometry, and 3D visualization, as well as for teachers demonstrating the relationship between spherical coordinates and parametric surfaces.