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八角形 - 钝角

八角形 - 钝角
几何画板及绘图内容加载中，请稍等……
2019-12-31 16:44
多边形角变换几何作图滑块动画
本范例展示了伊斯兰几何图案中的八角形构造。它涉及八边形的对称性和钝角特性。通过使用GeoGebra命令如Intersect、ConstructionStep、Point等，可以构造出复杂的几何图案。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(f) → C_3
  17. Midpoint(g) → D_3
  18. Midpoint(h) → E_3
  19. Midpoint(i) → F_3
  20. Midpoint(j) → G_3
  21. Midpoint(k) → H_3
  22. Midpoint(l) → I_3
  23. Midpoint(m) → J_3
  24. Segment(C_3, D_3) → g_5
  25. Segment(D_3, E_3) → h_5
  26. Segment(E_3, F_3) → i_5
  27. Segment(F_3, G_3) → j_5
  28. Segment(G_3, H_3) → k_5
  29. Segment(H_3, I_3) → l_5
  30. Segment(I_3, J_3) → m_5
  31. Segment(J_3, C_3) → n_5
  32. Centroid(veelhoek1) → K_3
  33. Mirror(CL, C_3) → CR
  34. Intersect(vgl1, n_5) → L_3
  35. Intersect(vgl1, k_5) → M_3
  36. Intersect(vgl2, j_5) → N_3
  37. Intersect(vgl2, g_5) → O_3
  38. Segment(M_3, CL) → p_5
  39. Segment(N_3, O_3) → q_5
  40. Rotate(M_3, 90°, K_3) → P_3
  41. Rotate(CL, 90°, K_3) → CL'
  42. Segment(P_3, CL') → r_5
  43. Rotate(N_3, 90°, K_3) → Q_3
  44. Rotate(O_3, 90°, K_3) → R_3
  45. Segment(Q_3, R_3) → s_5
  46. Rotate(M_3, 45°, K_3) → S_3
  47. Rotate(CL, 45°, K_3) → CL'_1
  48. Segment(S_3, CL'_1) → t_5
  49. Rotate(N_3, 45°, K_3) → T_3
  50. Rotate(O_3, 45°, K_3) → U_3
  51. Segment(T_3, U_3) → a_5
  52. Rotate(M_3, (-(45°)), K_3) → V_3
  53. Rotate(CL, (-(45°)), K_3) → CL'_2
  54. Segment(V_3, CL'_2) → b_5
  55. Rotate(N_3, (-(45°)), K_3) → W_3
  56. Rotate(O_3, (-(45°)), K_3) → Z_3
  57. Segment(W_3, Z_3) → c_5
  58. Intersect(a_5, b_5) → A_4
  59. Intersect(s_5, b_5) → B_4
  60. Intersect(p_5, veelhoek1) → C_4
  61. Intersect(p_5, s_5) → D_4
  62. Intersect(p_5, b_5) → E_4
  63. Intersect(t_5, b_5) → F_4
  64. Intersect(p_5, t_5) → G_4
  65. Intersect(p_5, r_5) → H_4
  66. Intersect(r_5, t_5) → I_4
  67. Intersect(t_5, c_5) → J_4
  68. Intersect(r_5, c_5) → K_4
  69. Intersect(q_5, r_5) → L_4
  70. Intersect(q_5, c_5) → M_4
  71. Intersect(a_5, c_5) → N_4
  72. Intersect(q_5, a_5) → O_4
  73. Intersect(q_5, s_5) → P_4
  74. Intersect(s_5, a_5) → Q_4
  75. PolyLine(G_3, M_3, O_4, N_3, G_3, E_4, F_4, G_4, L_3, C_3, O_3, M_4, N_4) → d_5
  76. Intersect(h_5, r_5) → R_4
  77. PolyLine(I_3, P_3, B_4, Q_3, I_3, I_4, J_4, K_4, R_4, E_3, R_3, Q_4, A_4) → e_5
  78. Intersect(g_5, t_5) → S_4
  79. PolyLine(H_3, S_3, Q_4, T_3, H_3, G_4, H_4, I_4, S_4, D_3, U_3, O_4, P_4) → f_6
  80. Intersect(m_5, b_5) → T_4
  81. PolyLine(F_3, V_3, M_4, W_3, F_3, B_4, D_4, E_4, T_4, J_3, Z_3, K_4, L_4) → g_6
  82. Vector(A, I) → hor
  83. Vector(A, F) → vert
  84. Sequence(Translate[Sequence[Translate[l1, Vector[(nn * hor)]], nn, 0, 3], Vector[(mm * vert)]], mm, -1, 1) → l2
  85. Polygon(N_1, O, K, J) → vierhoek1, h_6, o, k_6, j_6
  86. Sequence(Translate[Sequence[Polygon[Translate[N_1, Vector[(nn * hor)]], Translate[O, Vector[(nn * hor)]], Translate[K, Vector[(nn * hor)]], Translate[J, Vector[(nn * hor)]]], nn, -1, 1], Vector[(mm * vert)]], mm, 0, 1) → l3