对称性探索：通过几何构造发现图案规律

GeoGebra 命令及参数

1. Ray((0, 0), (1, 0)) → a
2. Point(a) → A
3. Mirror(B, a) → B'
4. Mirror(C, a) → C'
5. Mirror(D, a) → D'
6. Polygon(A, B', B) → poly1, b, a_1, b'
7. Polygon(C', C, D, D') → poly2, c', c, d, d'
8. Point(a) → Z
9. Mirror(H, a) → H'
10. Polygon(K, H, Z, H') → poly4, k, h, g, h'
11. Sequence(Polygon[Rotate[K, ((i * 360) * ° / N), K], Rotate[H, ((i * 360) * ° / N), K], Rotate[Z, ((i * 360) * ° / N), K], Rotate[H', ((i * 360) * ° / N), K]], i, 1, N) → list1
12. Sequence(Polygon[Rotate[A, ((i * 360) * ° / (N + f(1))), K], Rotate[B', ((i * 360) * ° / (N + f(1))), K], Rotate[B, ((i * 360) * ° / (N + f(1))), K]], i, 1, N + f(1)) → list2
13. Sequence(Polygon[Rotate[C', ((i * 360) * ° / (N + f(2))), K], Rotate[C, ((i * 360) * ° / (N + f(2))), K], Rotate[D, ((i * 360) * ° / (N + f(2))), K], Rotate[D', ((i * 360) * ° / (N + f(2))), K]], i, 1, N + f(2)) → list3
14. Textfield(f) → inputBox1
15. Polygon(E, G, L, F) → poly3, e, g_1, l, f_1
16. Sequence(Polygon[Rotate[E, ((i * 360) * ° / (N + f(3))), K], Rotate[G, ((i * 360) * ° / (N + f(3))), K], Rotate[L, ((i * 360) * ° / (N + f(3))), K], Rotate[F, ((i * 360) * ° / (N + f(3))), K]], i, 1, N + f(3)) → list4
17. Polygon(M, O, P) → poly5, p, m, o
18. Sequence(Polygon[Rotate[M, ((i * 360) * ° / (N + f(4))), K], Rotate[O, ((i * 360) * ° / (N + f(4))), K], Rotate[P, ((i * 360) * ° / (N + f(4))), K]], i, 1, N + f(4)) → list5