黄金矩形无限缩放——几何构造与视觉探索

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
3. Midpoint(h) → E
4. Circle(E, D) → c
5. Ray(B, C) → k
6. Intersect(c, k, 1) → F
7. OrthogonalLine(F, k) → l
8. OrthogonalLine(D, i) → m
9. Intersect(l, m) → G
10. Polygon(G, D, 4) → poly2, n, p, q, r, H, I
11. Segment(C, F) → s
12. Segment(F, I) → t
13. Polygon(F, I, 4) → poly3, a_{14}, b, d, e, J, K
14. Polygon(C, K, 4) → poly4, f_1, g_1, h_1, i_1, L, M
15. Polygon(H, M, 4) → poly5, j_1, k_1, l_1, m_1, N, O
16. Polygon(J, O, 4) → poly6, n_1, p_1, q_1, r_1, P, Q
17. Polygon(L, Q, 4) → poly7, s_1, t_1, a_1, b_1, R, S
18. Polygon(N, S, 4) → poly8, c_1, d_1, e_1, f_2, T, U
19. Polygon(P, U, 4) → poly9, g_2, h_2, i_2, j_2, V, W
20. Polygon(R, W, 4) → poly10, k_2, l_2, m_2, n_2, Z, A_1
21. Polygon(T, A_1, 4) → poly11, p_2, q_2, r_2, s_2, B_1, C_1
22. Polygon(V, C_1, 4) → poly12, t_2, a_2, b_2, c_2, D_1, E_1
23. Polygon(Z, E_1, 4) → poly13, d_2, e_2, f_3, g_3, F_1, G_1
24. Polygon(B_1, G_1, 4) → poly14, h_3, i_3, j_3, k_3, H_1, I_1
25. Polygon(D_1, I_1, 4) → poly15, l_3, m_3, n_3, p_3, J_1, K_1
26. Polygon(F_1, K_1, 4) → poly16, q_3, r_3, s_3, t_3, L_1, M_1
27. Polygon(H_1, M_1, 4) → poly17, a_3, b_3, c_3, d_3, N_1, O_1
28. Polygon(J_1, O_1, 4) → poly18, e_3, f_4, g_4, h_4, P_1, Q_1
29. Polygon(L_1, Q_1, 4) → poly19, i_4, j_4, k_4, l_4, R_1, S_1
30. Polygon(N_1, S_1, 4) → poly20, m_4, n_4, p_4, q_4, T_1, U_1
31. Polygon(P_1, U_1, 4) → poly21, r_4, s_4, t_4, a_4, V_1, W_1
32. Polygon(R_1, W_1, 4) → poly22, b_4, c_4, d_4, e_4, Z_1, A_2
33. Polygon(T_1, A_2, 4) → poly23, f_5, g_5, h_5, i_5, B_2, C_2
34. Polygon(V_1, C_2, 4) → poly24, j_5, k_5, l_5, m_5, D_2, E_2
35. Polygon(Z_1, E_2, 4) → poly25, n_5, p_5, q_5, r_5, F_2, G_2
36. Polygon(B_2, G_2, 4) → poly26, s_5, t_5, a_5, b_5, H_2, I_2
37. Polygon(D_2, I_2, 4) → poly27, c_5, d_5, e_5, f_6, J_2, K_2
38. Polygon(F_2, K_2, 4) → poly28, g_6, h_6, i_6, j_6, L_2, M_2
39. Polygon(H_2, M_2, 4) → poly29, k_6, l_6, m_6, n_6, N_2, O_2
40. Polygon(J_2, O_2, 4) → poly30, p_6, q_6, r_6, s_6, P_2, Q_2
41. Polygon(L_2, Q_2, 4) → poly31, t_6, a_6, b_6, c_6, R_2, S_2
42. Polygon(N_2, S_2, 4) → poly32, d_6, e_6, f_7, g_7, T_2, U_2
43. CircleArc(C, D, B) → c_7
44. CircleArc(H, I, D) → d_7
45. CircleArc(J, K, I) → e_7
46. CircleArc(L, M, K) → q_7
47. CircleArc(N, O, M) → r_7
48. CircleArc(P, Q, O) → s_7
49. CircleArc(R, S, Q) → t_7
50. CircleArc(T, U, S) → c_8
51. CircleArc(V, W, U) → d_8
52. CircleArc(Z, A_1, W) → e_8
53. CircleArc(B_1, C_1, A_1) → f_8
54. CircleArc(D_1, E_1, C_1) → g_8
55. CircleArc(F_1, G_1, E_1) → h_8
56. CircleArc(H_1, I_1, G_1) → k_8
57. CircleArc(J_1, K_1, I_1) → p_8
58. CircleArc(L_1, M_1, K_1) → q_8
59. CircleArc(N_1, O_1, M_1) → r_8
60. CircleArc(P_1, Q_1, O_1) → s_8
61. CircleArc(R_1, S_1, Q_1) → t_8
62. CircleArc(T_1, U_1, S_1) → c_9
63. CircleArc(V_1, W_1, U_1) → d_9
64. CircleArc(Z_1, A_2, W_1) → e_9
65. CircleArc(B_2, C_2, A_2) → f_9
66. CircleArc(D_2, E_2, C_2) → g_9
67. CircleArc(F_2, G_2, E_2) → h_9
68. CircleArc(H_2, I_2, G_2) → k_9
69. CircleArc(J_2, K_2, I_2) → p_9
70. CircleArc(L_2, M_2, K_2) → q_9
71. CircleArc(N_2, O_2, M_2) → r_9
72. CircleArc(P_2, Q_2, O_2) → h_7
73. CircleArc(R_2, S_2, Q_2) → k_7
74. CircleArc(T_2, U_2, S_2) → p_7
75. Polygon(P_2, U_2, 4) → poly33, i_7, j_7, l_7, m_7, V_2, W_2
76. Polygon(R_2, W_2, 4) → poly34, n_7, a_7, b_7, i_8, Z_2, A_3
77. CircleArc(V_2, W_2, U_2) → s_9
78. CircleArc(Z_2, A_3, W_2) → t_9
79. Segment(Z_2, T_2) → j_8
80. Segment(V_2, A_3) → l_8
81. Intersect(j_8, l_8) → B_3
82. Segment(B, F) → m_8
83. Segment(F, G) → n_8
84. Segment(G, A) → a_8
85. Polygon(F, B, 4) → poly35, b_8, i_9, j_9, l_9, C_3, D_3
86. CircleArc(F, B, D_3) → c_{10}
87. Polygon(G, D_3, 4) → poly36, m_9, n_9, a_9, b_9, E_3, F_3
88. Polygon(A, F_3, 4) → poly37, f_{10}, g_{10}, h_{10}, i_{10}, G_3, H_3
89. Polygon(C_3, H_3, 4) → poly38, j_{10}, k_{10}, l_{10}, m_{10}, I_3, J_3
90. Polygon(E_3, J_3, 4) → poly39, n_{10}, p_{10}, q_{10}, r_{10}, K_3, L_3
91. Polygon(G_3, L_3, 4) → poly40, s_{10}, t_{10}, a_{10}, b_{10}, M_3, N_3
92. Polygon(I_3, N_3, 4) → poly41, d_{10}, e_{10}, f_{11}, g_{11}, O_3, P_3
93. Polygon(K_3, P_3, 4) → poly42, h_{11}, i_{11}, j_{11}, k_{11}, Q_3, R_3
94. Polygon(M_3, R_3, 4) → poly43, l_{11}, m_{11}, n_{11}, p_{11}, S_3, T_3
95. Polygon(O_3, T_3, 4) → poly44, q_{11}, r_{11}, s_{11}, t_{11}, U_3, V_3
96. Polygon(Q_3, V_3, 4) → poly45, a_{11}, b_{11}, c_{11}, d_{11}, W_3, Z_3
97. Polygon(S_3, Z_3, 4) → poly46, e_{11}, f_{12}, g_{12}, h_{12}, A_4, B_4
98. Polygon(U_3, B_4, 4) → poly47, i_{12}, j_{12}, k_{12}, l_{12}, C_4, D_4
99. Polygon(W_3, D_4, 4) → poly48, m_{12}, n_{12}, p_{12}, q_{12}, E_4, F_4
100. Polygon(A_4, F_4, 4) → poly49, r_{12}, s_{12}, t_{12}, a_{12}, G_4, H_4
101. Polygon(C_4, H_4, 4) → poly50, b_{12}, c_{12}, d_{12}, e_{12}, I_4, J_4
102. Polygon(E_4, J_4, 4) → poly51, f_{13}, g_{13}, h_{13}, i_{13}, K_4, L_4
103. Polygon(G_4, L_4, 4) → poly52, j_{13}, k_{13}, l_{13}, m_{13}, M_4, N_4
104. Polygon(I_4, N_4, 4) → poly53, n_{13}, p_{13}, q_{13}, r_{13}, O_4, P_4
105. Polygon(K_4, P_4, 4) → poly54, s_{13}, t_{13}, a_{13}, b_{13}, Q_4, R_4
106. CircleArc(G, D_3, F_3) → c_{13}
107. CircleArc(A, F_3, H_3) → d_{13}
108. CircleArc(C_3, H_3, J_3) → e_{13}
109. CircleArc(E_3, J_3, L_3) → c_{14}
110. CircleArc(G_3, L_3, N_3) → d_{14}
111. CircleArc(I_3, N_3, P_3) → e_{14}
112. CircleArc(K_3, P_3, R_3) → f_{14}
113. CircleArc(M_3, R_3, T_3) → g_{14}
114. CircleArc(O_3, T_3, V_3) → h_{14}
115. CircleArc(Q_3, V_3, Z_3) → k_{14}
116. CircleArc(S_3, Z_3, B_4) → p_{14}
117. CircleArc(U_3, B_4, D_4) → q_{14}
118. CircleArc(W_3, D_4, F_4) → r_{14}
119. CircleArc(A_4, F_4, H_4) → s_{14}
120. CircleArc(C_4, H_4, J_4) → t_{14}
121. CircleArc(E_4, J_4, L_4) → c_{15}
122. CircleArc(G_4, L_4, N_4) → d_{15}
123. CircleArc(I_4, N_4, P_4) → e_{15}
124. CircleArc(K_4, P_4, R_4) → f_{15}
125. PointIn(poly54) → S_4
126. PointIn(poly54) → T_4
127. PointIn(poly53) → U_4
128. PointIn(poly52) → V_4
129. Segment(S_4, V_4) → i_{14}
130. Segment(V_4, U_4) → j_{14}
131. Segment(U_4, T_4) → l_{14}
132. Segment(T_4, S_4) → m_{14}