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重构吉尔希图案

重构吉尔希图案
几何画板及绘图内容加载中，请稍等……
2019-03-06 20:29
多边形解析几何
本范例演示了吉尔希瓷砖作为底层图案的重构过程。核心数学概念包括多边形、对称性和坐标几何。通过使用GeoGebra命令如Polygon、Intersect、PolyLine等，构建了复杂的几何图案。适合高中几何教学和兴趣探索。

GeoGebra 命令及参数

  1. Polygon(F_1, E_2, 5) → veelhoek12, d_2, e_2, f_3, g_3, h_3, F_2, G_2, H_2
  2. Polygon(Q, I, 5) → veelhoek4, b, c, d, e, f_1, R, S, T
  3. Polygon(F_5, T, G_5, H_5, I_5, J_5, K_5, F_2) → veelhoek27, d_6, t_8, e_6, f_7, g_7, h_7, i_7, j_7
  4. Intersect(g_7, h_7) → E_7
  5. Polygon(C, D, 5) → veelhoek1, f, g, h, i, j, E, F, G
  6. Polygon(H, I, 5) → veelhoek2, k, l, m, n, p, J, K, L
  7. Polygon(C, M, 5) → veelhoek3, q, r, s, t, a, N, O, P
  8. Polygon(U, V, 5) → veelhoek5, g_1, h_1, i_1, j_1, k_1, W, Z, A_1
  9. Polygon(B_1, V, 5) → veelhoek6, l_1, m_1, n_1, p_1, q_1, C_1, D_1, E_1
  10. Polygon(F_1, G_1, 5) → veelhoek7, r_1, s_1, t_1, a_1, b_1, H_1, I_1, J_1
  11. Polygon(K_1, L_1, 5) → veelhoek8, c_1, d_1, e_1, f_2, g_2, M_1, N_1, O_1
  12. Polygon(K_1, P_1, 5) → veelhoek9, h_2, i_2, j_2, k_2, l_2, Q_1, R_1, S_1
  13. Polygon(T_1, U_1, 5) → veelhoek10, m_2, n_2, p_2, q_2, r_2, V_1, W_1, Z_1
  14. Polygon(A_2, U_1, 5) → veelhoek11, s_2, t_2, a_2, b_2, c_2, B_2, C_2, D_2
  15. Polygon(I_2, J_2, 5) → veelhoek13, i_3, j_3, k_3, l_3, m_3, K_2, L_2, M_2
  16. Polygon(I_2, N_2, 5) → veelhoek14, n_3, p_3, q_3, r_3, s_3, O_2, P_2, Q_2
  17. Polygon(R_2, N_2, 5) → veelhoek15, t_3, a_3, b_3, c_3, d_3, S_2, T_2, U_2
  18. Polygon(V_2, W_2, 5) → veelhoek16, e_3, f_4, g_4, h_4, i_4, Z_2, A_3, B_3
  19. Polygon(C_3, W_2, 5) → veelhoek17, j_4, k_4, l_4, m_4, n_4, D_3, E_3, F_3
  20. Polygon(G_3, H_3, 5) → veelhoek18, p_4, q_4, r_4, s_4, t_4, I_3, J_3, K_3
  21. Polygon(L_3, M_3, 5) → veelhoek19, a_4, b_4, c_4, d_4, e_4, N_3, O_3, P_3
  22. Polygon(Q_3, M_3, 5) → veelhoek20, f_5, g_5, h_5, i_5, j_5, R_3, S_3, T_3
  23. Polygon(M_1, O, 5) → veelhoek22, q_5, r_5, s_5, t_5, a_5, Z_3, A_4, B_4
  24. Polygon(L_3, C_4, 5) → veelhoek23, b_5, c_5, d_5, e_5, f_6, D_4, E_4, F_4
  25. Polygon(D_4, G_4, 5) → veelhoek24, g_6, h_6, i_6, j_6, k_6, H_4, I_4, J_4
  26. Polygon(G_4, K_4, 5) → veelhoek25, l_6, m_6, n_6, p_6, q_6, L_4, M_4, N_4
  27. Polygon(H_1, P_2, 5) → veelhoek29, m_7, n_7, p_7, q_7, r_7, Z_4, A_5, B_5
  28. Polygon(O_3, E_1, 5) → veelhoek30, s_7, t_7, a_7, b_7, c_7, C_5, D_5, E_5
  29. Intersect(r_7, t_7) → O_4
  30. Intersect(p_7, b_7) → P_4
  31. Polygon(O_3, E_1, O_4, H_1, P_2, F_3, P_4, I_3) → veelhoek26, o_3, r_6, o_4, s_6, t_6, a_6, b_6, c_6
  32. Polygon(R_1, Q_4, R_4, S_4, C_2, L, T_4, E) → veelhoek28, k_7, l_7, d_7, e_7, f_8, l_8, g_8, e_8
  33. Polygon(U_4, A_2, 5) → veelhoek31, h_8, i_8, j_8, k_8, m_8, V_4, W_4, L_5
  34. Polygon(Q_5, B_3, R_5, S_5, T_5, U_5, V_5, W_5) → veelhoek33, s_8, a_8, b_8, c_8, d_8, u_5, v_5, w_5
  35. PolyLine(M_5, C_6, F_5, H_6, E_2, I_6, J_1, J_6, C_1, K_6, U, L_6, M, D_6, G, E_6, J, F_6, Q, G_6) → k_9
  36. Segment(N_4, M_6) → l_9
  37. Segment(N_4, M_4) → m_9
  38. Segment(M_4, N_6) → p_9
  39. Segment(N_6, M_6) → q_9
  40. Segment(M_4, O_6) → r_9
  41. Segment(O_6, K_3) → s_9
  42. Segment(K_3, P_6) → t_9
  43. Segment(P_6, D_3) → a_9
  44. Segment(D_3, Q_6) → b_9
  45. Segment(Q_6, V_2) → c_9
  46. Segment(V_2, R_6) → d_9
  47. Segment(R_6, Q_5) → e_9
  48. Segment(O_4, C_5) → f_{10}
  49. Segment(C_5, D_5) → g_{10}
  50. Segment(D_5, P_4) → h_{10}
  51. Segment(O_4, B_5) → i_{10}
  52. Segment(A_5, P_4) → j_{10}
  53. Segment(B_5, A_5) → k_{10}
  54. Intersect(i_1, j_1) → V_3
  55. Polygon(U_3, W_3, 5) → veelhoek21, k_5, l_5, m_5, n_5, p_5, S_6, T_6, U_6
  56. Polygon(Z_5, A_6, 5) → veelhoek32, n_8, p_8, q_8, r_8, f_9, B_6, V_6, W_6
  57. Intersect(r_5, s_5) → Z_6
  58. Segment(Z_6, A_7) → g_9
  59. Intersect(k_5, p_5) → B_7
  60. Segment(A_7, B_7) → h_9
  61. Point(k_9) → C_7
  62. Point(k_9) → D_7
  63. Segment(C_7, D_7) → i_9
  64. Intersect(f_3, g_3) → F_7
  65. Intersect(c_3, d_3) → H_7
  66. Intersect(g_4, h_4) → I_7
  67. Segment(H_7, I_7) → l_{10}
  68. Intersect(b_8, c_8) → J_7
  69. Polygon(U_7, E_7, 5) → veelhoek34, j_9, n_9, n_{10}, p_{10}, q_{10}, K_7, L_7, M_7
  70. Segment(I_7, J_7) → m_{10}
  71. Intersect(g_9, h_9) → N_7
  72. Intersect(r_5, s_5) → O_7
  73. Intersect(r, s) → Q_7
  74. Intersect(j_1, k_1) → R_7
  75. Intersect(k_5, p_5) → T_7
  76. Polygon(N_7, O_7, P_7, Q_7, C_7, R_7, S_7, T_7) → veelhoek35, r_{10}, o_7, s_{10}, t_{10}, a_{10}, b_{10}, c_{10}, d_{10}
  77. Polygon(V_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8) → veelhoek36, v_7, w_7, z_7, e_{10}, f_{11}, g_{11}, h_{11}, i_{11}
  78. PolyLine(V_8, U_8, H_8, G_8, F_8, I_8) → j_{11}
  79. PolyLine(W_8, Z_8, I_9, L_9, K_9, J_9) → k_{11}
  80. PolyLine(H_8, T_8, R_8, J_8, S_8, G_8) → l_{11}
  81. PolyLine(R_8, U_9, B_9, Q_8, K_8, J_8) → m_{11}
  82. PolyLine(U_9, A_9, C_9, E_9, D_9, B_9) → n_{11}
  83. PolyLine(D_9, P_8, M_8, L_8, Q_8, B_9) → p_{11}
  84. PolyLine(C_9, G_9, Q_9, R_9, F_9, E_9) → q_{11}
  85. PolyLine(A_9, H_9, O_9, P_9, G_9, C_9) → r_{11}
  86. PolyLine(H_9, M_9, I_9, L_9, N_9, O_9) → s_{11}
  87. Segment(I_8, V_8) → t_{11}
  88. Segment(W_8, J_9) → a_{11}
  89. Segment(U_8, Z_8) → b_{11}
  90. Segment(F_9, S_9) → c_{11}
  91. Segment(R_9, T_9) → d_{11}
  92. Segment(M_8, N_8) → e_{11}
  93. Segment(P_8, O_8) → f_{12}
  94. Segment(V_9, J_9) → g_{12}