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伊斯兰几何图案中的其他瓷砖构造

伊斯兰几何图案中的其他瓷砖构造
几何画板及绘图内容加载中，请稍等……
2019-12-31 16:09
圆多边形变换几何作图
该范例演示了如何利用GeoGebra构造伊斯兰风格的几何瓷砖图案，通过多边形、点与折线等基本元素生成对称且重复的装饰性图形。核心数学概念包括对称性、外接圆、整数坐标、向量以及算术平均，这些概念共同支撑了图案的规律性与美感。作图要点在于使用Polygon命令创建基础多边形，Point命令定位关键顶点，PolyLine命令绘制折线边界，并通过多个多边形（veelhoek1、veelhoek2、veelhoek3）及其关联对象（如c、d、e、f等）的嵌套与复制，形成复杂的镶嵌结构。该范例适合中学或大学阶段的几何教学，也可用于艺术设计或数学文化课程，帮助学生理解几何变换与对称在图案设计中的应用。

GeoGebra 命令及参数

  1. Polygon(C, D, E, F, G, H) → veelhoek1, c, d, e, f, g, h
  2. Polygon(C, I, J, K, L, M) → veelhoek2, c_1, i, j, k, l, m
  3. Polygon(C, H, G, N, L, M) → veelhoek3, c_2, h_1, g_1, n, l_1, m_1
  4. Polygon(O, D, C, I, P, Q, R, S, T, U) → veelhoek4, o, u, d_1, c_3, i_1, p, q, r, s, t
  5. Polygon(S, R, V, W, Z, A_1) → veelhoek5, s_1, r_1, v, w, z_1, a_1
  6. Polygon(T, S, B_1, C_1, D_1, E_1) → veelhoek6, t_1, s_2, b_1, a, b, e_1
  7. Polygon(S, A_1, Z, F_1, C_1, B_1) → veelhoek7, s_3, f_1, z_2, j_1, k_1, n_1
  8. Polygon(F, G, N, G_1, H_1) → veelhoek8, f_2, g_2, n_2, p_1, q_1
  9. Polygon(P, I, J, K) → vierhoek1, p_2, i_2, j_2, k_2
  10. Polygon(O, D, E, F) → vierhoek2, o_1, d_2, e_2, f_3
  11. Polygon(W, V, R, Q) → vierhoek3, w_1, v_1, r_2, q_2
  12. Polygon(D_1, E_1, T, U) → vierhoek4, h_2, l_2, t_2, u_1
  13. Polygon(D_1, C_1, F_1, I_1, J_1) → veelhoek9, m_2, a_2, b_2, g_3, h_3
  14. Polygon(I_1, F_1, Z, W, K_1) → veelhoek10, i_3, j_3, z_3, w_2, k_3
  15. Polygon(K, L, N, G_1, L_1) → veelhoek11, k_4, l_3, n_3, m_3, p_3
  16. Polygon(F_1, M_1, N_1, O_1, P_1, Q_1, T, S, A_1, Z) → veelhoek12, q_3, z_4, r_3, t_3, a_3, b_3, d_3, t_4, s_4, e_3
  17. Polygon(R_1, S_1, T_1, U_1, V_1) → veelhoek13, f_4, g_4, h_4, i_4, j_4
  18. Point(e_3) → A_2
  19. Polygon(W_1, Z_1, A_2, B_2, C_2) → veelhoek14, l_4, m_4, n_4, p_4, q_4
  20. Point(d_3) → E_2
  21. Point(t) → F_2
  22. Point(s) → H_2
  23. Polygon(D_2, E_2, F_2, G_2, H_2) → veelhoek15, r_4, a_4, b_4, c_4, d_4
  24. Point(q) → J_2
  25. Point(r) → M_2
  26. Polygon(I_2, J_2, K_2, L_2, M_2) → veelhoek16, e_4, f_5, g_5, h_5, i_5
  27. Point(o) → N_2
  28. Point(d_1) → Q_2
  29. Polygon(N_2, O_2, P_2, Q_2, R_2) → veelhoek17, j_5, o_2, k_5, l_5, m_5
  30. Point(s_4) → U_2
  31. Polygon(S_2, H_2, T_2, M_2, U_2) → veelhoek18, n_5, p_5, q_5, r_5, u_2
  32. Point(c_3) → Z_2
  33. Polygon(Q_2, V_2, W_2, Z_2, A_3) → veelhoek19, s_5, v_2, t_5, a_5, b_5
  34. Point(i_1) → E_3
  35. Polygon(B_3, Z_2, C_3, D_3, E_3) → veelhoek20, c_5, d_5, e_5, f_6, g_6
  36. Point(p) → F_3
  37. Polygon(F_3, G_3, E_3, H_3, I_3) → veelhoek21, h_6, i_6, j_6, k_6, l_6
  38. Polygon(J_2, J_3, F_3, K_3, L_3) → veelhoek22, m_6, n_6, p_6, q_6, r_6
  39. Point(u) → M_3
  40. PolyLine(M_3, N_3, F_2, O_3) → s_6
  41. PolyLine(M_3, P_3, N_2, Q_3) → t_6
  42. PolyLine(R_3, T_1, S_3, T_3) → a_6
  43. Polygon(U_3, V_3, W_3, Z_3, Z_1) → veelhoek23, u_3, v_3, w_3, b_6, c_6
  44. Polygon(A_4, V_3, B_4, C_4, D_4) → veelhoek24, d_6, e_6, f_7, g_7, h_7
  45. Polygon(E_4, F_4, G_4, H_4, I_4) → veelhoek25, i_7, j_7, k_7, l_7, m_7
  46. Polygon(J_4, K_4, L_3, L_4, M_4) → veelhoek26, n_7, p_7, q_7, r_7, s_7
  47. Polygon(N_4, O_4, P_4, Q_4, R_4) → veelhoek27, t_7, o_4, a_7, b_7, c_7
  48. Polygon(S_4, M_4, T_4, O_4, U_4) → veelhoek28, d_7, e_7, f_8, g_8, u_4
  49. Polygon(V_4, W_4, Z_4, A_5, B_5) → veelhoek29, v_4, w_4, h_8, i_8, j_8
  50. Polygon(H_3, C_5, D_5, E_5, F_5) → veelhoek30, k_8, l_8, m_8, n_8, p_8
  51. Polygon(G_5, H_5, I_5, J_5, K_5) → veelhoek31, q_8, r_8, s_8, t_8, a_8
  52. Polygon(L_5, E_5, M_5, N_5, H_5) → veelhoek32, b_8, c_8, d_8, e_8, f_9
  53. Polygon(W_3, O_5, J_4, P_5, S_4, Q_5, B_4, R_5) → veelhoek33, g_9, o_5, h_9, i_9, j_9, k_9, l_9, m_9
  54. Polygon(H_4, S_5, U_4, T_5, N_4, U_5, V_5, W_5) → veelhoek34, n_9, p_9, q_9, r_9, s_9, u_5, v_5, w_5
  55. Polygon(D_5, Z_5, A_6, B_6, C_6, D_6, M_5, E_6) → veelhoek35, t_9, z_5, a_9, b_9, c_9, d_9, e_9, f_{10}
  56. Polygon(N_5, G_6, F_6, H_6, I_6, J_6, I_5, K_6) → veelhoek36, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
  57. Polygon(C_6, P_6, Q_6, R_6, S_6) → veelhoek37, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}
  58. Polygon(F_6, L_6, M_6, N_6, O_6) → veelhoek38, a_{10}, b_{10}, c_{10}, d_{10}, o_6
  59. Polygon(R_6, T_6, U_6, V_6, M_6) → veelhoek39, e_{10}, f_{11}, u_6, v_6, g_{11}
  60. Polygon(A_6, W_6, Z_6, A_7, P_6) → veelhoek40, h_{11}, w_6, z_6, i_{11}, j_{11}
  61. Polygon(B_7, I_6, O_6, C_7) → vierhoek5, k_{11}, l_{11}, m_{11}, n_{11}
  62. Polygon(F_7, G_7, K_5, H_7) → vierhoek6, p_{11}, q_{11}, r_{11}, s_{11}
  63. Polygon(D_7, Q_4, E_7, F_7) → vierhoek7, t_{11}, a_{11}, b_{11}, c_{11}
  64. Polygon(I_7, I_4, V_5, J_7) → vierhoek8, d_{11}, e_{11}, f_{12}, g_{12}
  65. Polygon(K_7, L_7, M_7, N_7, O_7) → veelhoek41, h_{12}, i_{12}, j_{12}, k_{12}, o_7
  66. Polygon(P_7, Q_7, R_7, S_7, T_7, U_7) → veelhoek42, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, u_7