Octagons - Obtuse

Octagons - Obtuse
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2019-12-31 16:44
This example demonstrates the construction of Islamic geometric patterns using octagons. It involves the symmetry and obtuse angle properties of octagons. Using GeoGebra commands such as Intersect, ConstructionStep, and Point, complex geometric patterns can be constructed. Suitable for middle school and above students to learn geometric construction and symmetry.

GeoGebra Commands & Parameters

  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