大卫之星参数化构造

大卫之星参数化构造
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2019-12-05 13:07
①本范例演示了如何通过参数化方法构造大卫之星(Star of David)的几何图形;②涉及的核心数学概念包括参数方程、等边三角形、几何变换、相似与放缩;③作图要点——从下方『构造摘要』提炼用到了Polygon(多边形)、Intersect(交点)、Point(点)等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解参数曲线与几何作图的结合应用。

GeoGebra 命令及参数

  1. Polygon(A, C, D) → t1, d, a, c
  2. Polygon(E, F, G) → t2, g, e, f
  3. Intersect(d, f) → H
  4. Intersect(c, g) → I
  5. Point(e) → J
  6. Polygon(H, I, J) → t3, j, h, i
  7. Intersect(c, f) → K
  8. Intersect(d, e) → L
  9. Intersect(a, g) → M
  10. Polygon(K, L, M) → t4, m, k, l
  11. Polygon(E, A, G, C, F, D) → poly1, e_1, a_1, g_1, c_1, f_1, d_1
  12. Polygon(A, N, G, S, E, O, D, P, F, Q, C, R) → poly2, a_2, r, g_2, s, n, e_2, o, d_2, p, f_2, q, c_2
  13. Point(m) → T
  14. Intersect(h, l) → U
  15. Intersect(i, k) → V
  16. Polygon(T, U, V) → t5, v, t, u
  17. Intersect(j, l) → W
  18. Intersect(i, m) → Z
  19. Intersect(h, k) → A_1
  20. Polygon(W, Z, A_1) → t6, b, w, z_1
  21. Intersect(v, b) → B_1
  22. Intersect(t, z_1) → C_1
  23. Intersect(u, w) → D_1
  24. Polygon(B_1, C_1, D_1) → t7, h_1, b_1, i_1
  25. Intersect(u, b) → E_1
  26. Intersect(v, z_1) → F_1
  27. Intersect(t, w) → G_1
  28. Polygon(E_1, F_1, G_1) → t8, j_1, k_1, l_1
  29. Intersect(i_1, j_1) → H_1
  30. Intersect(h_1, k_1) → I_1
  31. Intersect(b_1, l_1) → J_1
  32. Polygon(H_1, I_1, J_1) → t9, m_1, n_1, p_1
  33. Intersect(h_1, j_1) → K_1
  34. Intersect(i_1, l_1) → L_1
  35. Intersect(b_1, k_1) → M_1
  36. Polygon(K_1, L_1, M_1) → t10, q_1, r_1, s_1
  37. Intersect(m_1, q_1) → N_1
  38. Intersect(n_1, s_1) → O_1
  39. Intersect(p_1, r_1) → P_1
  40. Polygon(N_1, O_1, P_1) → t11, t_1, h_2, o_1
  41. Intersect(p_1, q_1) → Q_1
  42. Intersect(m_1, s_1) → R_1
  43. Intersect(n_1, r_1) → S_1
  44. Polygon(Q_1, R_1, S_1) → t12, i_2, j_2, k_2
  45. Intersect(o_1, i_2) → T_1
  46. Intersect(t_1, j_2) → U_1
  47. Intersect(h_2, k_2) → V_1
  48. Polygon(T_1, U_1, V_1) → t13, v_1, l_2, u_1
  49. Intersect(t_1, i_2) → W_1
  50. Intersect(h_2, j_2) → Z_1
  51. Intersect(o_1, k_2) → A_2
  52. Polygon(W_1, Z_1, A_2) → t14, m_2, w_1, n_2
  53. Intersect(v_1, n_2) → B_2
  54. Intersect(l_2, m_2) → C_2
  55. Intersect(u_1, w_1) → D_2
  56. Polygon(B_2, C_2, D_2) → t15, p_2, b_2, q_2
  57. Intersect(l_2, w_1) → E_2
  58. Intersect(v_1, m_2) → F_2
  59. Intersect(u_1, n_2) → G_2
  60. Polygon(E_2, F_2, G_2) → t16, r_2, s_2, t_2
  61. Intersect(p_2, s_2) → H_2
  62. Intersect(b_2, r_2) → I_2
  63. Intersect(q_2, t_2) → J_2
  64. Polygon(H_2, I_2, J_2) → t17, f_3, g_3, h_3
  65. Intersect(q_2, s_2) → K_2
  66. Intersect(p_2, r_2) → L_2
  67. Intersect(b_2, t_2) → M_2
  68. Polygon(K_2, L_2, M_2) → t18, i_3, j_3, k_3
  69. Intersect(h_3, i_3) → N_2
  70. Intersect(f_3, j_3) → O_2
  71. Intersect(g_3, k_3) → P_2
  72. Polygon(N_2, O_2, P_2) → t19, l_3, m_3, o_2
  73. Intersect(g_3, j_3) → Q_2
  74. Intersect(f_3, i_3) → R_2
  75. Intersect(h_3, k_3) → S_2
  76. Polygon(Q_2, R_2, S_2) → t20, n_3, p_3, q_3
  77. Intersect(l_3, p_3) → T_2
  78. Intersect(m_3, n_3) → U_2
  79. Intersect(o_2, q_3) → V_2
  80. Polygon(T_2, U_2, V_2) → t21, v_2, r_3, u_2
  81. Intersect(o_2, p_3) → W_2
  82. Intersect(l_3, n_3) → Z_2
  83. Intersect(m_3, q_3) → A_3
  84. Polygon(W_2, Z_2, A_3) → t22, a_3, w_2, z_2
  85. Intersect(u_2, a_3) → B_3
  86. Intersect(v_2, w_2) → C_3
  87. Intersect(r_3, z_2) → D_3
  88. Polygon(B_3, C_3, D_3) → t23, d_3, b_3, c_3
  89. Intersect(u_2, z_2) → E_3
  90. Intersect(v_2, a_3) → F_3
  91. Intersect(r_3, w_2) → G_3
  92. Polygon(E_3, F_3, G_3) → t24, s_3, e_3, t_3

AI 绘图提示语参考

绘制一个大卫之星的几何构造图,包含两个相互交织的六边形,通过等边三角形、缩放和参数曲线构建。先画出两个六边形,再找到它们的交点,用这些点构造新的三角形,逐步形成星形图案。最终图形应展示出对称性和几何美感,体现参数方程和几何变换的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。