Rainbow Reflection on a Circle: Mirror Images as a Parameterized Sequence

This example demonstrates a “rainbow” pattern of reflected lines on a circle: as the driving point/direction varies with a parameter, consecutive mirror reflections are constructed, producing an ordered band-like visual trace. Key math ideas include circle geometry (often in the unit-circle setting), reflection (mirror transformation), and parameterization/iteration that turns a single reflection rule into a reflected sequence. Construction is built with GeoGebra commands from the summary: Circle to create the circle; Mirror to compute reflected rays or segments with respect to a chosen geometric element; Length to measure the relevant segments; and Element-style object management (e.g., hue, button1, O, t, g, C0/C1/C2, L_1, f, n, and many points A1, A2, …) to plot multiple reflection outputs in succession. Suitable for middle/high school geometry, interactive classroom demonstrations, and exploratory learning focused on reflection properties and parameter-driven geometric construction.