Cn Symmetry: Rotational and Mirror Symmetry Visualization

This GeoGebra example dynamically demonstrates Cn symmetry, where a figure coincides with itself after a rotation of 360°/n. The core mathematical concepts include rotational symmetry, mirror reflection, angle measurement, and the generation of symmetry groups. The construction uses GeoGebra commands such as Line, Rotate, Angle, and Mirror. Starting with points A, B and line f, it applies rotation to create angle α and point B', then mirroring to produce line g and point C. Repeated rotations and reflections generate f', g', f'', C', C'', C''', D, D', D'', D''' and other objects, visually revealing the iterative pattern of symmetric transformations. This is suitable for upper secondary and undergraduate students learning symmetry, transformation geometry, and introductory group theory, as well as for teachers creating interactive lessons to illustrate the combination of rotational and mirror symmetries.