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正八边形构造

正八边形构造
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2019-12-31 16:40
多边形角向量几何作图
本范例展示了伊斯兰几何图案中的正八边形构造。涉及的核心数学概念包括角度、向量和几何作图。通过使用GeoGebra命令如Intersect、ConstructionStep、Point等，可以构造出正八边形。适合初中及以上学生学习几何作图和对称性。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Point(xAxis) → B
  4. Polygon(A, B, 8) → veelhoek1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  5. Polygon(D, C, 8) → veelhoek2, n, J, K, L, M, N, p, q, r, s, t, a, b, I
  6. Polygon(L, K, 8) → veelhoek3, c, P, Q, R, S, T, d, e, f_1, g_1, h_1, i_1, j_1, O
  7. Polygon(R, Q, 8) → veelhoek4, k_1, V, W, Z, A_1, B_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, U
  8. Polygon(B, A, 8) → veelhoek5, t_1, D_1, E_1, F_1, G_1, H_1, a_1, b_1, c_1, d_1, e_1, f_2, g_2, C_1
  9. Polygon(J, I, 8) → veelhoek6, h_2, J_1, K_1, L_1, M_1, N_1, i_2, j_2, k_2, l_2, m_2, n_2, p_2, I_1
  10. Polygon(P, O, 8) → veelhoek7, q_2, P_1, Q_1, R_1, S_1, T_1, r_2, s_2, t_2, a_2, b_2, c_2, d_2, O_1
  11. Polygon(V, U, 8) → veelhoek8, e_2, V_1, W_1, Z_1, A_2, B_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, U_1
  12. Polygon(F, E, 8) → veelhoek9, m_3, D_2, E_2, F_2, G_2, H_2, n_3, p_3, q_3, r_3, s_3, t_3, a_3, C_2
  13. Polygon(N, M, 8) → veelhoek10, b_3, J_2, K_2, L_2, M_2, N_2, c_3, d_3, e_3, f_4, g_4, h_4, i_4, I_2
  14. Polygon(T, S, 8) → veelhoek11, j_4, P_2, Q_2, R_2, S_2, T_2, k_4, l_4, m_4, n_4, p_4, q_4, r_4, O_2
  15. Polygon(B_1, A_1, 8) → veelhoek12, s_4, V_2, W_2, Z_2, A_3, B_3, t_4, a_4, b_4, c_4, d_4, e_4, f_5, U_2
  16. Midpoint(j) → C_3
  17. Midpoint(k) → D_3
  18. Midpoint(l) → E_3
  19. Midpoint(m) → F_3
  20. Midpoint(f) → G_3
  21. Midpoint(g) → H_3
  22. Midpoint(h) → I_3
  23. Midpoint(i) → J_3
  24. Segment(C_3, F_3) → g_5
  25. Segment(D_3, G_3) → h_5
  26. Segment(E_3, H_3) → i_5
  27. Segment(F_3, I_3) → j_5
  28. Segment(G_3, J_3) → k_5
  29. Segment(H_3, C_3) → l_5
  30. Segment(I_3, D_3) → m_5
  31. Segment(J_3, E_3) → n_5
  32. Segment(C_3, F_3) → p_5
  33. Midpoint(s) → K_3
  34. Midpoint(p) → L_3
  35. Midpoint(a) → M_3
  36. Midpoint(b) → N_3
  37. Midpoint(q) → O_3
  38. Midpoint(r) → P_3
  39. Midpoint(t) → Q_3
  40. Midpoint(i_2) → R_3
  41. Midpoint(f_2) → S_3
  42. Midpoint(k_2) → T_3
  43. Midpoint(l_2) → U_3
  44. Midpoint(m_2) → V_3
  45. Midpoint(n_2) → W_3
  46. Midpoint(p_2) → Z_3
  47. Midpoint(g_2) → A_4
  48. Midpoint(a_1) → B_4
  49. Midpoint(b_1) → C_4
  50. Midpoint(c_1) → D_4
  51. Midpoint(d_1) → E_4
  52. Midpoint(e_1) → F_4
  53. Segment(M_3, L_3) → q_5
  54. Segment(N_3, O_3) → r_5
  55. Segment(I_3, P_3) → s_5
  56. Segment(L_3, K_3) → t_5
  57. Segment(O_3, Q_3) → a_5
  58. Segment(P_3, M_3) → b_5
  59. Segment(K_3, N_3) → c_5
  60. Segment(Q_3, I_3) → d_5
  61. Segment(G_3, D_4) → e_5
  62. Segment(B_4, E_4) → f_6
  63. Segment(C_4, F_4) → g_6
  64. Segment(D_4, S_3) → h_6
  65. Segment(E_4, A_4) → i_6
  66. Segment(F_4, G_3) → j_6
  67. Segment(S_3, B_4) → k_6
  68. Segment(A_4, C_4) → l_6
  69. Segment(O_3, T_3) → m_6
  70. Segment(R_3, U_3) → n_6
  71. Segment(S_3, V_3) → p_6
  72. Segment(T_3, W_3) → q_6
  73. Segment(U_3, Z_3) → r_6
  74. Segment(V_3, O_3) → s_6
  75. Segment(W_3, R_3) → t_6
  76. Segment(Z_3, S_3) → a_6
  77. Line(E_3, H_3) → b_6
  78. Line(K_3, L_3) → c_6
  79. Intersect(b_6, c_6) → G_4
  80. Segment(H_3, G_4) → d_6
  81. Segment(L_3, G_4) → e_6
  82. Line(C_3, H_3) → f_7
  83. Line(M_3, L_3) → g_7
  84. Line(C_4, A_4) → h_7
  85. Line(W_3, R_3) → i_7
  86. Line(E_4, A_4) → j_7
  87. Line(U_3, R_3) → k_7
  88. Intersect(i_7, h_7) → H_4
  89. Intersect(g_7, k_7) → I_4
  90. Intersect(f_7, j_7) → J_4
  91. Segment(H_3, J_4) → l_7
  92. Segment(A_4, J_4) → m_7
  93. Segment(A_4, H_4) → n_7
  94. Segment(L_3, I_4) → p_7
  95. Segment(H_4, R_3) → q_7
  96. Segment(R_3, I_4) → r_7
  97. Intersect(m_5, n_5) → K_4
  98. Intersect(m_5, p_5) → L_4
  99. Intersect(n_5, p_5) → M_4
  100. Intersect(h_5, n_5) → N_4
  101. Intersect(h_5, p_5) → O_4
  102. Intersect(i_5, p_5) → P_4
  103. Intersect(h_5, i_5) → Q_4
  104. Intersect(h_5, j_5) → R_4
  105. Intersect(i_5, j_5) → S_4
  106. Intersect(i_5, k_5) → T_4
  107. Intersect(j_5, k_5) → U_4
  108. Intersect(j_5, l_5) → V_4
  109. Intersect(k_5, l_5) → W_4
  110. Intersect(k_5, m_5) → Z_4
  111. Intersect(l_5, m_5) → A_5
  112. Intersect(l_5, n_5) → B_5
  113. PolyLine(K_4, L_4, U_4, V_4, W_4, Z_4, A_5, B_5, K_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4) → s_7
  114. PolyLine(C_3, L_4, H_3, V_4, I_3, Z_4, J_3, B_5, C_3, D_3, N_4, E_3, P_4, F_3, R_4, G_3, T_4) → t_7
  115. Midpoint(C_3, G_3) → D_5
  116. Polygon(C_3, L_4, K_4, B_5) → vierhoek1, a_7, b_7, c_7, d_7
  117. Sequence(Polygon[Rotate[C_3, (nn * 45°), D_5], Rotate[L_4, (nn * 45°), D_5], Rotate[K_4, (nn * 45°), D_5], Rotate[B_5, (nn * 45°), D_5]], nn, 0, 7) → l1
  118. Polygon(L_3, G_4, H_3, J_4, A_4, H_4, R_3, I_4) → veelhoek13, e_7, f_8, g_8, h_8, i_8, j_8, k_8, l_8
  119. Vector(A, I) → hot
  120. Vector(A, F) → vert
  121. Sequence(Translate[Sequence[Translate[l1, Vector[(nn * hot)]], nn, 0, 3], Vector[(mm * vert)]], mm, -1, 1) → l2
  122. Sequence(Translate[Sequence[Polygon[Translate[L_3, Vector[(nn * hot)]], Translate[G_4, Vector[(nn * hot)]], Translate[H_3, Vector[(nn * hot)]], Translate[J_4, Vector[(nn * hot)]], Translate[A_4, Vector[(nn * hot)]], Translate[H_4, Vector[(nn * hot)]], Translate[R_3, Vector[(nn * hot)]], Translate[I_4, Vector[(nn * hot)]]], nn, 0, 2], Vector[(mm * vert)]], mm, 0, 1) → l3
  123. Polygon(B, H_1, I, C) → vierhoek2, b_8, m_8, i_9, c_8
  124. Sequence(Translate[Sequence[Polygon[Translate[B, Vector[(nn * hot)]], Translate[H_1, Vector[(nn * hot)]], Translate[I, Vector[(nn * hot)]], Translate[C, Vector[(nn * hot)]]], nn, 0, 2], Vector[(mm * vert)]], mm, 0, 1) → l4

AI 绘图提示语参考

绘制一个由多个正八边形组成的伊斯兰几何图案，这些八边形围绕中心点相互连接，形成对称的星形结构。图案中心是两个正交的轴线的交点，从中心点向外扩展多个正八边形，每个八边形的边与相邻八边形的边相交，形成复杂的几何图案。注意保持图案的对称性和几何精确性。
以上提示语为根据原始绘图命令整理而来，仅供参考。