吉里赫图案拼图：对称与几何变换的交互探索

GeoGebra 命令及参数

1. Point(Circle[A, 1]) → B
2. Polygon(A, B, 10) → veelhoek1, f, p, C, D, E, F, G, H, I, J, g, h, i, j, k, l, m, n
3. Midpoint(f) → K
4. Midpoint(i) → L
5. Midpoint(g) → M
6. Midpoint(h) → O
7. Midpoint(p) → P
8. Segment(K, L) → q
9. Segment(O, P) → r
10. Intersect(q, r) → N
11. OrthogonalLine(K, f) → s
12. Mirror(N, s) → N'
13. Segment(N', K) → t
14. Segment(K, N) → a
15. Centroid(veelhoek1) → Q
16. Sequence(Rotate[{a, t}, (nn * 36°), Q], nn, 1, 10) → l1
17. Point(Circle[R, 1]) → S
18. Polygon(R, S, 5) → veelhoek2, b, c, d, e, f_1, T, U, V
19. Midpoint(b) → W
20. Rotate(S, 54°, W) → S'
21. Midpoint(c) → Z
22. Ray(W, S') → g_1
23. Rotate(S, (-(54°)), Z) → S'_1
24. Ray(Z, S'_1) → h_1
25. Intersect(g_1, h_1) → A_1
26. Segment(W, A_1) → i_1
27. Segment(A_1, Z) → j_1
28. Centroid(veelhoek2) → B_1
29. Sequence(Rotate[{i_1, j_1}, (nn * 72°), B_1], nn, 1, 5) → l2
30. Point(Circle[C_1, 1]) → D_1
31. Rotate(C_1, 144°, D_1) → E_1
32. Rotate(D_1, 72°, C_1) → F_1
33. Rotate(D_1, (-(72°)), E_1) → G_1
34. Rotate(C_1, 72°, F_1) → H_1
35. Polygon(F_1, C_1, D_1, E_1, G_1, H_1) → veelhoek3, k_1, c_1, d_1, e_1, l_1, m_1
36. Midpoint(m_1) → I_1
37. Midpoint(k_1) → J_1
38. Midpoint(c_1) → K_1
39. Midpoint(l_1) → L_1
40. Midpoint(e_1) → M_1
41. Midpoint(d_1) → N_1
42. Segment(J_1, K_1) → n_1
43. Rotate(J_1, (-(72°)), K_1) → O_1
44. Rotate(K_1, (-(72°)), K_1) → P_1
45. Segment(O_1, P_1) → p_1
46. Segment(J_1, M_1) → q_1
47. Intersect(p_1, q_1) → Q_1
48. Segment(H_1, D_1) → r_1
49. Mirror(Q_1, r_1) → R_1
50. PolyLine(J_1, K_1, Q_1, I_1, J_1) → s_1
51. Mirror(J_1, r_1) → S_1
52. Mirror(K_1, r_1) → T_1
53. Mirror(Q_1, r_1) → U_1
54. Mirror(I_1, r_1) → V_1
55. Mirror(J_1, r_1) → W_1
56. PolyLine(S_1, T_1, U_1, V_1, W_1) → t_1
57. Point(Circle[Z_1, 1]) → A_2
58. Rotate(Z_1, 144°, A_2) → B_2
59. Rotate(A_2, (-(144°)), Z_1) → C_2
60. Segment(B_2, C_2) → a_1
61. Mirror(A_2, a_1) → D_2
62. Mirror(Z_1, a_1) → E_2
63. Polygon(B_2, A_2, Z_1, C_2, E_2, D_2) → veelhoek4, b_2, a_2, z_1, c_2, e_2, d_2
64. Midpoint(b_2) → F_2
65. Midpoint(d_2) → G_2
66. Midpoint(a_2) → H_2
67. Midpoint(z_1) → I_2
68. Rotate(A_2, 54°, F_2) → J_2
69. Ray(F_2, J_2) → b_1
70. Rotate(A_2, (-(54°)), H_2) → K_2
71. Ray(H_2, K_2) → f_2
72. Intersect(b_1, f_2) → L_2
73. Mirror(L_2, a_1) → M_2
74. Midpoint(e_2) → N_2
75. Segment(H_2, N_2) → g_2
76. Mirror(L_2, g_2) → O_2
77. Mirror(M_2, g_2) → P_2
78. Midpoint(c_2) → Q_2
79. PolyLine(F_2, L_2, F_2, H_2, O_2, I_2, Q_2, P_2, N_2, M_2, G_2) → h_2
80. Point(Circle[R_2, 1]) → S_2
81. Rotate(R_2, 72°, S_2) → T_2
82. Rotate(S_2, (-(108°)), R_2) → U_2
83. Polygon(S_2, R_2, U_2, T_2) → vierhoek1, s_2, r_2, u_2, t_2
84. Midpoint(s_2) → V_2
85. Midpoint(t_2) → W_2
86. Midpoint(u_2) → Z_2
87. Midpoint(r_2) → A_3
88. Rotate(W_2, (-(72°)), V_2) → B_3
89. Ray(V_2, B_3) → i_2
90. Segment(R_2, T_2) → j_2
91. Mirror(B_3, j_2) → C_3
92. Ray(A_3, C_3) → k_2
93. Intersect(i_2, j_2) → D_3
94. Segment(S_2, U_2) → l_2
95. Mirror(D_3, l_2) → E_3
96. PolyLine(V_2, D_3, A_3, Z_2, E_3, W_2, V_2) → m_2