Art of Rotation with Segments: Mirror-Driven Circular Structures

This GeoGebra example demonstrates how to start from a segmented polyline and then apply rotational constructions (and auxiliary mirroring) to generate structured, symmetric patterns around a center. The key mathematical ideas include Circle geometry (center and radius), Rotation as a transformation with stepwise repetition, and Mirror symmetry to relate corresponding points and segments. Depending on the setup, the construction also highlights the periodic nature that connects well with Trigonometric Functions and angle/radius parameter choices. Construction-wise, it leverages the commands in the build: Sequence to generate the required point sequence for repeated transforms; Max to control bounds/selection of parameter extremes; Point to define the center O and multiple control points P1…P8 (plus list-generated points such as P0/P8); PolyLine to form the initial segmented path; Circle to create the base reference circle; and Mirror to produce symmetric counterparts that help assemble the final pattern. Lists such as liste11, listeP1, listeP2, and listeP3, together with parameters (e.g., r_i, r_e, R, a, v, A, b), organize the rotation/mirroring workflow into a clean circular design. Suitable for middle to early university geometry lessons, interactive classroom demos, and student explorations of transformations and visualization.