Islamic Geometric Patterns by chris cambré (3)

Islamic Geometric Patterns by chris cambré (3)
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2019-12-31 20:59
This example demonstrates the construction of Islamic geometric patterns. Key mathematical concepts include symmetry, intersection, and geometric construction. Using GeoGebra commands such as Point, CircleArc, Polygon, PolyLine, Segment, and Intersect, complex geometric patterns can be created. Suitable for middle school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → H
  2. Point(xAxis) → I
  3. CircleArc(G, H, I) → c
  4. Polygon(V_1, U_1, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, A_2, Z_1, W_1, B_2, C_2, D_2, Q_2, F_2, G_2, H_2) → veelhoek1, v_1, h_2, i_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, a_2, u_1, z_1, w_1, b_2, c_2, d_2, q_2, f_2, g_2
  5. Polygon(S_2, I, S_1, E_2, R_2, C_2) → veelhoek2, s_2, i, s_1, e_2, r_2, f
  6. Polygon(T_1, J, B_3, H_1, T_2, U_2, V_2, W_2, Z_2, G_2, A_3) → veelhoek3, t_1, a_3, b_3, j, h_1, t_2, u_2, v_2, w_2, z_2, g
  7. Polygon(Q_1, C_3, O, D_3, M_2, E_3, F_3, G_3, H_3, I_3, I_1) → veelhoek4, q_1, i_1, o, c_3, d_3, h, e_3, f_3, g_3, h_3, i_3
  8. Polygon(B_3, Q_2, E_2, L_3) → vierhoek1, k, l, m, l_3
  9. Polygon(O_2, C_3, K_3, J_3) → vierhoek2, n, p, k_3, j_3
  10. Polygon(I_2, W_2, O_3, P_3) → vierhoek3, q, r, o_3, p_3
  11. Polygon(F_3, K_2, N_3, M_3) → vierhoek4, s, t, n_3, m_3
  12. Polygon(O_3, Q_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, H_3, I_4, U_2, M_3, J_4, R_3, S_3, T_3, U_3, V_3, W_3, Z_3) → veelhoek5, d, z_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, f_1, q_3, i_4, g_1, j_4, e, r_3, s_3, t_3, u_3, v_3, w_3
  13. Polygon(U_3, F_1, E_1) → driehoek1, e_1, j_1, k_1
  14. Polygon(D_1, K_4, W_3, T_4, E_1, K, L, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4) → veelhoek6, d_1, s_4, l_1, t_4, m_1, k_5, l_5, k_4, l_4, m_4, n_4, o_4, p_4, q_4, r_4
  15. Polygon(B_1, A_1, V_4) → driehoek2, v_4, b_1, a_1
  16. Polygon(V_4, W_4, H_5, I_5, J_5, K_5, L_4, L_5, U_4, M_5, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5) → veelhoek7, n_1, g_5, h_5, i_5, j_5, p_1, r_1, c_1, u_4, m_5, w_4, z_4, a_5, b_5, c_5, d_5, e_5, f_5
  17. Polygon(A_1, W, N_5, O_5, P_5, Q_5, Z_4, R_5) → veelhoek8, n_5, w, p_5, o_5, q_5, r_5, s_5, t_5
  18. Polygon(N_5, S_5, U, T_5, U_5, V_5, V, W_5, Z_5, A_6) → veelhoek9, f_6, a_6, g_6, u, h_6, u_5, v_5, v, w_5, z_5
  19. Polygon(U_5, S, B_6, T) → vierhoek5, i_6, s_6, b_6, t_6
  20. Polygon(Q, P, R, B_6) → vierhoek6, q_6, p_6, r_6, j_6
  21. Polygon(O_1, C_6, B_5, D_6, P_5, E_6, Z_5, Z) → veelhoek10, o_1, c_6, k_6, d_6, l_6, e_6, m_6, z_6
  22. Polygon(P_1, D_5, O_1) → driehoek3, n_6, f_7, g_7
  23. Polygon(L_1, F_6, H_5, M_6, M_1, M, N, C_4, G_6, H_6, I_6, P_4, J_6, K_6, L_6) → veelhoek11, h_7, r_7, s_7, t_7, a_7, m_8, n_8, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7
  24. PolyLine(I, S_1, D_1, C_1, B_1, A_1, T_1, J, H_1, G_1, F_1, E_1, K, L) → b_7
  25. PolyLine(O_1, P_1, O, Q_1, R_1, H, N_1, M_1, M, N, L_1, K_1, J_1, I_1) → c_7
  26. PolyLine(A_1, W, O_1, U, S, Q, P, R, T, V, Z) → d_7
  27. Point(c) → N_6
  28. Polygon(H, N_6, A_2, O_6, J_3, R_1) → veelhoek12, h_8, e_7, f_8, o_6, g_8, i_8
  29. Point(c) → P_6
  30. Polygon(I, S_1, D_1, C_1, B_1, A_1, W, U, S, Q, P, R, T_1, T, V, Z, O_1, P_1, N_1, M_1, M, N, L_1, J, K_1, J_1, I_1, O, Q_1, R_1, H, N_6, P_6, S_2, H_1, G_1, F_1, E_1, K, L) → veelhoek13, j_8, b_8, c_8, d_8, e_8, f_9, g_9, h_9, i_9, j_9, k_9, k_8, l_9, m_9, n_9, p_9, q_9, r_9, s_9, t_9, a_9, b_9, l_8, c_9, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, p_8, m_{10}, q_8, r_8, s_8, t_8, a_8
  31. Segment(N_1, F_5) → n_{10}
  32. Segment(U_4, C_1) → p_{10}
  33. Segment(K_1, E_4) → q_{10}
  34. Polygon(K_1, E_4, L_1) → driehoek4, r_{10}, s_{10}, t_{10}
  35. Segment(L_1, E_4) → a_{10}
  36. Polygon(I_1, G_4, J_1) → driehoek5, b_{10}, c_{10}, d_{10}
  37. Polygon(G_1, S_3, H_1) → driehoek6, e_{10}, f_{11}, g_{11}
  38. Polygon(M_1, F_5, N_1) → driehoek7, h_{11}, i_{11}, j_{11}
  39. Polygon(D_1, C_1, U_4) → driehoek8, k_{11}, l_{11}, m_{11}
  40. Intersect(c, k_{10}, 2) → Q_6
  41. Point(xAxis) → R_6
  42. Point(xAxis) → B_7
  43. Polygon(Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7) → veelhoek14, n_{11}, a_{11}, p_{11}, q_{11}, r_{11}, u_6, v_6, w_6, s_{11}, t_{11}
  44. Point(b_7) → C_7
  45. Segment(T_6, C_7) → b_{11}
  46. Point(k_8) → D_7
  47. Segment(S_6, D_7) → c_{11}
  48. Point(h_{10}) → E_7
  49. Segment(Z_6, E_7) → d_{11}
  50. Point(h_{10}) → F_7
  51. Segment(A_7, F_7) → e_{11}
  52. Polygon(G_7, H_7, Q_7, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7) → veelhoek15, f_{12}, n_{12}, b_{13}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, o_7
  53. Segment(Q_7, W_6) → q_{12}
  54. Segment(H_7, U_6) → r_{12}
  55. Point(h_7) → R_7
  56. Point(s_9) → W_7
  57. PolyLine(R_7, N_7, M_7, S_7, T_7, U_7, V_7, W_7) → p_{12}
  58. Point(j_1) → Z_7
  59. Point(b_7) → C_8
  60. PolyLine(Z_7, K_7, L_7, S_7, T_7, A_8, B_8, C_8) → s_{12}
  61. PolyLine(B_8, D_8, E_8, F_8, G_8, H_8, V_7, U_7, A_8) → t_{12}
  62. Point(f_7) → I_8
  63. Point(n_9) → K_8
  64. PolyLine(I_8, G_8, F_8, J_8, K_8) → a_{12}
  65. Point(v_4) → L_8
  66. Point(g_9) → M_8
  67. PolyLine(L_8, E_8, F_8, J_8, M_8) → b_{12}
  68. Point(m_9) → N_8
  69. Point(h_9) → O_8
  70. Segment(N_8, O_8) → c_{12}

AI Drawing Prompt Reference

Create a complex symmetric Islamic geometric pattern. Start by placing two points on a horizontal axis and drawing a circular arc through them. Then, arrange a series of polygons—triangles, quadrilaterals, and higher-order polygons—around the arc and axis, interlocking and nesting to form star-like and petal-shaped motifs. Use polylines to outline the main skeletal framework of the pattern. Place additional points on the arc and connect them to polygon vertices with segments, creating internal subdivisions. Finally, add new points on the axis and construct a large polygon incorporating them, while selecting points from the polylines and polygons to draw connecting segments, completing the intricate symmetrical design.
The prompt above was compiled from the original drawing commands and is for reference only.