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Other Tiles: Islamic Geometric Patterns Construction

Other Tiles: Islamic Geometric Patterns Construction
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2019-12-31 16:09
CirclePolygonTransformationGeometric Construction
This GeoGebra example demonstrates the construction of Islamic-style geometric tile patterns using basic elements such as polygons, points, and polylines. The core mathematical concepts involved include symmetry, circumscribed circles, integers, vectors, and arithmetic mean, which together contribute to the regularity and aesthetic appeal of the patterns. The construction utilizes the Polygon command to create base polygons, Point to define key vertices, and PolyLine to draw boundary segments. Multiple polygons (veelhoek1, veelhoek2, veelhoek3) and their associated objects (c, d, e, f, etc.) are nested and replicated to form a complex tessellation. This example is suitable for middle school to university-level geometry lessons, as well as for art design or mathematical culture courses, helping students understand how geometric transformations and symmetry are applied in pattern design.

GeoGebra Commands & Parameters

  1. Polygon(C, D, E, F, G, H) → veelhoek1, c, d, e, f, g, h
  2. Polygon(C, I, J, K, L, M) → veelhoek2, c_1, i, j, k, l, m
  3. Polygon(C, H, G, N, L, M) → veelhoek3, c_2, h_1, g_1, n, l_1, m_1
  4. Polygon(O, D, C, I, P, Q, R, S, T, U) → veelhoek4, o, u, d_1, c_3, i_1, p, q, r, s, t
  5. Polygon(S, R, V, W, Z, A_1) → veelhoek5, s_1, r_1, v, w, z_1, a_1
  6. Polygon(T, S, B_1, C_1, D_1, E_1) → veelhoek6, t_1, s_2, b_1, a, b, e_1
  7. Polygon(S, A_1, Z, F_1, C_1, B_1) → veelhoek7, s_3, f_1, z_2, j_1, k_1, n_1
  8. Polygon(F, G, N, G_1, H_1) → veelhoek8, f_2, g_2, n_2, p_1, q_1
  9. Polygon(P, I, J, K) → vierhoek1, p_2, i_2, j_2, k_2
  10. Polygon(O, D, E, F) → vierhoek2, o_1, d_2, e_2, f_3
  11. Polygon(W, V, R, Q) → vierhoek3, w_1, v_1, r_2, q_2
  12. Polygon(D_1, E_1, T, U) → vierhoek4, h_2, l_2, t_2, u_1
  13. Polygon(D_1, C_1, F_1, I_1, J_1) → veelhoek9, m_2, a_2, b_2, g_3, h_3
  14. Polygon(I_1, F_1, Z, W, K_1) → veelhoek10, i_3, j_3, z_3, w_2, k_3
  15. Polygon(K, L, N, G_1, L_1) → veelhoek11, k_4, l_3, n_3, m_3, p_3
  16. Polygon(F_1, M_1, N_1, O_1, P_1, Q_1, T, S, A_1, Z) → veelhoek12, q_3, z_4, r_3, t_3, a_3, b_3, d_3, t_4, s_4, e_3
  17. Polygon(R_1, S_1, T_1, U_1, V_1) → veelhoek13, f_4, g_4, h_4, i_4, j_4
  18. Point(e_3) → A_2
  19. Polygon(W_1, Z_1, A_2, B_2, C_2) → veelhoek14, l_4, m_4, n_4, p_4, q_4
  20. Point(d_3) → E_2
  21. Point(t) → F_2
  22. Point(s) → H_2
  23. Polygon(D_2, E_2, F_2, G_2, H_2) → veelhoek15, r_4, a_4, b_4, c_4, d_4
  24. Point(q) → J_2
  25. Point(r) → M_2
  26. Polygon(I_2, J_2, K_2, L_2, M_2) → veelhoek16, e_4, f_5, g_5, h_5, i_5
  27. Point(o) → N_2
  28. Point(d_1) → Q_2
  29. Polygon(N_2, O_2, P_2, Q_2, R_2) → veelhoek17, j_5, o_2, k_5, l_5, m_5
  30. Point(s_4) → U_2
  31. Polygon(S_2, H_2, T_2, M_2, U_2) → veelhoek18, n_5, p_5, q_5, r_5, u_2
  32. Point(c_3) → Z_2
  33. Polygon(Q_2, V_2, W_2, Z_2, A_3) → veelhoek19, s_5, v_2, t_5, a_5, b_5
  34. Point(i_1) → E_3
  35. Polygon(B_3, Z_2, C_3, D_3, E_3) → veelhoek20, c_5, d_5, e_5, f_6, g_6
  36. Point(p) → F_3
  37. Polygon(F_3, G_3, E_3, H_3, I_3) → veelhoek21, h_6, i_6, j_6, k_6, l_6
  38. Polygon(J_2, J_3, F_3, K_3, L_3) → veelhoek22, m_6, n_6, p_6, q_6, r_6
  39. Point(u) → M_3
  40. PolyLine(M_3, N_3, F_2, O_3) → s_6
  41. PolyLine(M_3, P_3, N_2, Q_3) → t_6
  42. PolyLine(R_3, T_1, S_3, T_3) → a_6
  43. Polygon(U_3, V_3, W_3, Z_3, Z_1) → veelhoek23, u_3, v_3, w_3, b_6, c_6
  44. Polygon(A_4, V_3, B_4, C_4, D_4) → veelhoek24, d_6, e_6, f_7, g_7, h_7
  45. Polygon(E_4, F_4, G_4, H_4, I_4) → veelhoek25, i_7, j_7, k_7, l_7, m_7
  46. Polygon(J_4, K_4, L_3, L_4, M_4) → veelhoek26, n_7, p_7, q_7, r_7, s_7
  47. Polygon(N_4, O_4, P_4, Q_4, R_4) → veelhoek27, t_7, o_4, a_7, b_7, c_7
  48. Polygon(S_4, M_4, T_4, O_4, U_4) → veelhoek28, d_7, e_7, f_8, g_8, u_4
  49. Polygon(V_4, W_4, Z_4, A_5, B_5) → veelhoek29, v_4, w_4, h_8, i_8, j_8
  50. Polygon(H_3, C_5, D_5, E_5, F_5) → veelhoek30, k_8, l_8, m_8, n_8, p_8
  51. Polygon(G_5, H_5, I_5, J_5, K_5) → veelhoek31, q_8, r_8, s_8, t_8, a_8
  52. Polygon(L_5, E_5, M_5, N_5, H_5) → veelhoek32, b_8, c_8, d_8, e_8, f_9
  53. Polygon(W_3, O_5, J_4, P_5, S_4, Q_5, B_4, R_5) → veelhoek33, g_9, o_5, h_9, i_9, j_9, k_9, l_9, m_9
  54. Polygon(H_4, S_5, U_4, T_5, N_4, U_5, V_5, W_5) → veelhoek34, n_9, p_9, q_9, r_9, s_9, u_5, v_5, w_5
  55. Polygon(D_5, Z_5, A_6, B_6, C_6, D_6, M_5, E_6) → veelhoek35, t_9, z_5, a_9, b_9, c_9, d_9, e_9, f_{10}
  56. Polygon(N_5, G_6, F_6, H_6, I_6, J_6, I_5, K_6) → veelhoek36, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
  57. Polygon(C_6, P_6, Q_6, R_6, S_6) → veelhoek37, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}
  58. Polygon(F_6, L_6, M_6, N_6, O_6) → veelhoek38, a_{10}, b_{10}, c_{10}, d_{10}, o_6
  59. Polygon(R_6, T_6, U_6, V_6, M_6) → veelhoek39, e_{10}, f_{11}, u_6, v_6, g_{11}
  60. Polygon(A_6, W_6, Z_6, A_7, P_6) → veelhoek40, h_{11}, w_6, z_6, i_{11}, j_{11}
  61. Polygon(B_7, I_6, O_6, C_7) → vierhoek5, k_{11}, l_{11}, m_{11}, n_{11}
  62. Polygon(F_7, G_7, K_5, H_7) → vierhoek6, p_{11}, q_{11}, r_{11}, s_{11}
  63. Polygon(D_7, Q_4, E_7, F_7) → vierhoek7, t_{11}, a_{11}, b_{11}, c_{11}
  64. Polygon(I_7, I_4, V_5, J_7) → vierhoek8, d_{11}, e_{11}, f_{12}, g_{12}
  65. Polygon(K_7, L_7, M_7, N_7, O_7) → veelhoek41, h_{12}, i_{12}, j_{12}, k_{12}, o_7
  66. Polygon(P_7, Q_7, R_7, S_7, T_7, U_7) → veelhoek42, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, u_7