Implicit Surface 3D Test: Piecewise Functions and Natural Number Sequences in Sp

① This example demonstrates the construction and visualization of a 3D implicit surface, using GeoGebra's sequence commands to generate multiple surface slices that reveal the spatial form of a complex mathematical expression. ② Core mathematical concepts include implicit surfaces, piecewise functions, natural number sequences, tangent functions, quadrilaterals, and cosine functions, which together build a periodic and piecewise-defined solid shape. ③ Construction highlights: from the summary, the Sequence command is used to generate sequence objects (n, t, tz, ty, tx), with lists listex, listey, listez defined, along with buttons Bouton1, Bouton2, Bouton3 and parameters a, b, c, p, spd for interactive control and dynamic changes. ④ Suitable for high school to university-level mathematics learners, this example aids in exploring 3D representations of implicit equations, geometric meanings of function combinations, and advanced GeoGebra plotting techniques, serving as a case for mathematical experiments or computer-assisted instruction.