Symmetry Numbers & Parabolic Mirror: Geometric Transformations

This GeoGebra example dynamically illustrates a geometric construction combining symmetry numbers with a parabolic mirror. It demonstrates how, based on the focus-directrix property of a parabola, a series of symmetric points and polygons are generated through rotations and reflections, using angles, segments, and intersections to form a mirror-symmetric pattern. Core mathematical concepts include the optical property of parabolas (parallel rays reflecting through the focus), symmetry transformations (rotation and reflection), geometric ratios and number patterns, as well as circumscribed/inscribed circles and polygons. The construction uses GeoGebra commands such as Line, Parabola, Circle, Point, Segment, Rotate, Angle, and Intersect, creating objects like A, B, C, f, c, a, H, d, M, i, M', α, k, M'', β, l, M''', γ, m, N, δ, n, N', ε, p, D, g, h, E, j, F, q, G, r, I, s, J, t, K, and b, with successive rotations and angle markings to build the symmetric design. It is suitable for high school and above students exploring geometric transformations, parabola properties, and symmetry aesthetics, and can be used in math labs or interdisciplinary art-math teaching.