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伊玛目鼓膜图案

伊玛目鼓膜图案
几何画板及绘图内容加载中，请稍等……
2019-12-31 22:23
多边形变换几何作图
这个范例演示了伊斯兰几何图案的构造。核心数学概念包括几何作图、多边形和变换。使用了Polygon、Centroid、Midpoint、Segment、Intersect、Sequence、Translate、Point、PolyLine、Mirror等GeoGebra命令。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Polygon(G, H, I, E, F) → veelhoek1, g, h, i, e, f
  2. Centroid(veelhoek1) → K_1
  3. Polygon(G, J, K, L, M) → veelhoek2, g_1, j, k, l, m
  4. Centroid(veelhoek2) → L_1
  5. Polygon(L_1, K_1, 10) → veelhoek3, n, d, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, p, q, r, s, t, a, b, c
  6. Polygon(K_1, L_1, 10) → veelhoek4, f_1, q_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1
  7. Polygon(V_1, U_1, 10) → veelhoek5, r_1, g_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, s_1, t_1, a_1, b_1, c_1, d_1, e_1, f_2
  8. Polygon(F_2, S_1, 10) → veelhoek6, h_2, r_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2
  9. Polygon(U_1, L_1, T_1, S_1, F_2, E_2) → veelhoek7, u_1, s_2, t_2, a_2, b_2, e_2
  10. Polygon(P, Q, L, N, O) → veelhoek8, p_3, q_3, l_3, n_3, o
  11. Polygon(F_1, E_1, D_1, C_1, S) → veelhoek9, c_2, d_2, f_3, g_3, s_3
  12. Polygon(Z, U, C_1, B_1, A_1) → veelhoek10, z_1, u, h_3, i_3, j_3
  13. Polygon(E_1, J_1, I_1, H_1, G_1) → veelhoek11, k_3, m_3, r_3, t_3, a_3
  14. Polygon(V, N, W, K, R, S, T, U) → veelhoek12, v, n_4, w, k_4, r_4, s_4, t_4, u_2
  15. Midpoint(H_2, G_2) → U_2
  16. Segment(N, U_2) → b_3
  17. Midpoint(L_2, V_1) → V_2
  18. Segment(U, V_2) → c_3
  19. Midpoint(K_2, L_2) → W_2
  20. Segment(W_2, N) → d_3
  21. Segment(P, A_1) → e_3
  22. Intersect(c_3, e_3) → Z_2
  23. Centroid(veelhoek5) → A_3
  24. Polygon(N, V, Z_2, O) → vierhoek1, n_5, v_1, z_2, o_1
  25. Sequence(Polygon[Rotate[N, (nn * 36°), A_3], Rotate[V, (nn * 36°), A_3], Rotate[Z_2, (nn * 36°), A_3], Rotate[O, (nn * 36°), A_3]], nn, 1, 10) → l1
  26. Centroid(veelhoek6) → B_3
  27. Translate(l1, Vector[A_3, B_3]) → l1'
  28. Centroid(veelhoek4) → C_3
  29. Translate(l1, Vector[A_3, C_3]) → l1'_1
  30. Centroid(veelhoek3) → D_3
  31. Translate(l1, Vector[A_3, D_3]) → l1'_2
  32. Point(l1'_1) → E_3
  33. Point(l1'_2) → F_3
  34. Point(l1) → G_3
  35. PolyLine(E_3, F_3, W, G_3, E_3) → f_4
  36. Mirror(E_3, yAxis) → H_3
  37. Mirror(E_3, yAxis) → K_3
  38. Point(l1') → I_3
  39. Point(l1'_2) → J_3
  40. PolyLine(I_3, U, T, J_3, I_3) → g_4
  41. Translate(U_1, Vector[A_3, B_3]) → L_3
  42. Translate(L_1, Vector[A_3, B_3]) → M_3
  43. Translate(T_1, Vector[A_3, B_3]) → N_3
  44. Translate(S_1, Vector[A_3, B_3]) → O_3
  45. Translate(F_2, Vector[A_3, B_3]) → P_3
  46. Translate(E_2, Vector[A_3, B_3]) → Q_3
  47. Polygon(L_3, M_3, N_3, O_3, P_3, Q_3) → veelhoek7', h_4, i_4, j_4, o_3, l_4, m_4
  48. Translate(U_1, Vector[A_3, C_3]) → R_3
  49. Translate(L_1, Vector[A_3, C_3]) → S_3
  50. Translate(T_1, Vector[A_3, C_3]) → T_3
  51. Translate(S_1, Vector[A_3, C_3]) → U_3
  52. Translate(F_2, Vector[A_3, C_3]) → V_3
  53. Translate(E_2, Vector[A_3, C_3]) → W_3
  54. Polygon(R_3, S_3, T_3, U_3, V_3, W_3) → veelhoek7'_1, p_4, q_4, a_4, u_3, v_3, w_3
  55. Translate(E_3, Vector[A_3, B_3]) → Z_3
  56. Translate(F_3, Vector[A_3, B_3]) → A_4
  57. Translate(W, Vector[A_3, B_3]) → W'
  58. Translate(G_3, Vector[A_3, B_3]) → B_4
  59. Translate(E_3, Vector[A_3, B_3]) → C_4
  60. PolyLine(Z_3, A_4, W', B_4, C_4) → b_4
  61. Translate(I_3, Vector[A_3, B_3]) → D_4
  62. Translate(U, Vector[A_3, B_3]) → U'
  63. Translate(T, Vector[A_3, B_3]) → T'
  64. Translate(J_3, Vector[A_3, B_3]) → E_4
  65. Translate(I_3, Vector[A_3, B_3]) → F_4
  66. Translate(E_3, Vector[A_3, C_3]) → G_4
  67. Translate(F_3, Vector[A_3, C_3]) → H_4
  68. Translate(W, Vector[A_3, C_3]) → W'_1
  69. Translate(G_3, Vector[A_3, C_3]) → I_4
  70. Translate(E_3, Vector[A_3, C_3]) → J_4
  71. Translate(I_3, Vector[A_3, C_3]) → K_4
  72. Translate(U, Vector[A_3, C_3]) → U'_1
  73. Translate(T, Vector[A_3, C_3]) → T'_1
  74. Translate(J_3, Vector[A_3, C_3]) → L_4
  75. Translate(I_3, Vector[A_3, C_3]) → M_4
  76. PolyLine(K_4, U'_1, T'_1, L_4, M_4) → e_4

AI 绘图提示语参考

绘制一个伊斯兰风格鼓面图案。先构造两个相交的五边形，分别取其中心，以两中心为顶点构造两个正十边形，再以其中一个十边形的边构造另一个十边形，形成旋转对称的星形结构。随后在周围添加多个五边形和十边形，形成外圈装饰。连接特定中点形成线段，并找出交点，构造一个四边形。以该四边形为基本单元，绕其中心旋转复制十份，形成环形阵列。再将此阵列平移至其他三个十边形的中心，得到四组对称图案。最后用折线连接各阵列上的点，并沿纵轴镜像，完成整体对称的几何装饰图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。