10/3和10/4多边形

10/3和10/4多边形
几何画板及绘图内容加载中,请稍等……
2019-12-31 16:23
该范例展示了伊斯兰几何图案中的10/3和10/4多边形。涉及的核心数学概念包括多边形、对称性、四边形、二次方程、逻辑。通过使用GeoGebra命令如构造步骤、旋转、多边形、点、中点、线段、交点、多边形等进行作图。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. ConstructionStep() → stap
  2. Rotate(A, 36°) → A'
  3. Polygon(A, A', 10) → veelhoek1, f, p, B, C, D, E, F, G, H, I, g, h, i, j, k, l, m, n
  4. Point(xAxis) → J
  5. Rotate(K, 36°, J) → K'
  6. Polygon(K, K', 10) → veelhoek2, q, f_1, L, M, N, P, Q, R, S, T, r, s, t, a, b, c, d, e
  7. Midpoint(f) → U
  8. Midpoint(g) → V
  9. Midpoint(h) → W
  10. Midpoint(i) → Z
  11. Midpoint(j) → A_1
  12. Midpoint(k) → B_1
  13. Midpoint(l) → C_1
  14. Midpoint(m) → D_1
  15. Midpoint(n) → E_1
  16. Midpoint(p) → F_1
  17. Midpoint(q) → G_1
  18. Midpoint(r) → H_1
  19. Midpoint(s) → I_1
  20. Midpoint(t) → J_1
  21. Midpoint(a) → K_1
  22. Midpoint(b) → L_1
  23. Midpoint(c) → M_1
  24. Midpoint(d) → N_1
  25. Midpoint(e) → O_1
  26. Midpoint(f_1) → P_1
  27. Segment(U, Z) → g_1
  28. Segment(G_1, K_1) → h_1
  29. Segment(V, A_1) → i_1
  30. Segment(H_1, L_1) → j_1
  31. Segment(W, B_1) → k_1
  32. Segment(I_1, M_1) → l_1
  33. Segment(Z, C_1) → m_1
  34. Segment(J_1, N_1) → n_1
  35. Segment(A_1, D_1) → p_1
  36. Segment(K_1, O_1) → q_1
  37. Segment(B_1, E_1) → r_1
  38. Segment(L_1, P_1) → s_1
  39. Segment(C_1, F_1) → t_1
  40. Segment(M_1, G_1) → a_1
  41. Segment(D_1, U) → b_1
  42. Segment(N_1, H_1) → c_1
  43. Segment(E_1, V) → d_1
  44. Segment(O_1, I_1) → e_1
  45. Segment(F_1, W) → f_2
  46. Segment(P_1, J_1) → g_2
  47. Intersect(b_1, yAxis) → Q_1
  48. Intersect(d_1, f_2) → R_1
  49. Intersect(g_1, d_1) → S_1
  50. Intersect(g_1, f_2) → T_1
  51. Intersect(i_1, f_2) → U_1
  52. Intersect(g_1, xAxis) → V_1
  53. Intersect(g_1, k_1) → W_1
  54. Intersect(i_1, k_1) → Z_1
  55. Intersect(i_1, m_1) → A_2
  56. Intersect(k_1, m_1) → B_2
  57. Intersect(k_1, p_1) → C_2
  58. Intersect(p_1, m_1) → D_2
  59. Intersect(m_1, r_1) → E_2
  60. Intersect(p_1, r_1) → F_2
  61. Intersect(p_1, t_1) → G_2
  62. Intersect(r_1, t_1) → H_2
  63. Intersect(r_1, b_1) → I_2
  64. Intersect(t_1, b_1) → J_2
  65. Intersect(t_1, d_1) → K_2
  66. Intersect(b_1, d_1) → L_2
  67. Intersect(s_1, e_1) → M_2
  68. Intersect(a_1, e_1) → N_2
  69. Intersect(a_1, g_2) → O_2
  70. Intersect(c_1, g_2) → P_2
  71. Intersect(h_1, c_1) → Q_2
  72. Intersect(h_1, e_1) → R_2
  73. Intersect(j_1, e_1) → S_2
  74. Intersect(j_1, g_2) → T_2
  75. Intersect(l_1, g_2) → U_2
  76. Intersect(h_1, l_1) → V_2
  77. Intersect(h_1, n_1) → W_2
  78. Intersect(j_1, n_1) → Z_2
  79. Intersect(j_1, q_1) → A_3
  80. Intersect(l_1, q_1) → B_3
  81. Intersect(l_1, s_1) → C_3
  82. Intersect(n_1, s_1) → D_3
  83. Intersect(n_1, a_1) → E_3
  84. Intersect(q_1, a_1) → F_3
  85. Intersect(q_1, c_1) → G_3
  86. Intersect(s_1, c_1) → H_3
  87. PolyLine(Q_1, R_1, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, S_1, Q_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2) → h_2
  88. PolyLine(O_2, P_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, M_2, N_2, Q_2, O_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2) → i_2
  89. PolyLine(Q_1, U, C_2, B_1, E_2, C_1, G_2, D_1, I_2, E_1, K_2, F_1, S_1, Q_1, V, U_1, W, W_1, Z, A_2, A_1) → j_2
  90. PolyLine(O_2, G_1, A_3, L_1, C_3, M_1, E_3, N_1, G_3, O_1, M_2, P_1, Q_2, O_2, H_1, S_2, I_1, U_2, J_1, W_2, K_1) → k_2

AI 绘图提示语参考

绘制两个旋转36度的十边形,并找出各边中点,连接相邻中点形成新的多边形,最后交点处绘制辅助线,展示对称和几何变换的图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。