Border Tile

Border Tile
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2015-07-28 06:14
This example demonstrates how to draw a border tile pattern using GeoGebra. Key mathematical concepts include geometry, squares, triangles, and dilation. Using commands like Polygon and objects, complex geometric shapes can be constructed. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Polygon(E, F, G, H) → poly2, e, f, g, h
  3. Polygon(E_1, F_1, G_1, H_1) → poly2_1, e_1, f_1, g_1, h_1
  4. Polygon(E_2, F_2, G_2, H_2) → poly2_2, e_2, f_2, g_2, h_2
  5. Polygon(E_3, F_3, G_3, H_3) → poly2_3, e_3, f_3, g_3, h_3
  6. Polygon(E_4, F_4, G_4, H_4) → poly2_4, e_4, f_4, g_4, h_4
  7. Polygon(E_5, F_5, G_5, H_5) → poly2_5, e_5, f_5, g_5, h_5
  8. Polygon(E_6, F_6, G_6, H_6) → poly2_6, e_6, f_6, g_6, h_6
  9. Polygon(E_7, F_7, G_7, H_7) → poly2_7, e_7, f_7, g_7, h_7
  10. Polygon(E_8, F_8, G_8, H_8) → poly2_8, e_8, f_8, g_8, h_8
  11. Polygon(E_9, F_9, G_9, H_9) → poly2_9, e_9, f_9, g_9, h_9
  12. Polygon(I, J, K) → poly3, k, i, j
  13. Polygon(I_1, J_1, K_1) → poly3_1, k_1, i_1, j_1
  14. Polygon(I_2, J_2, K_2) → poly3_2, k_2, i_2, j_2
  15. Polygon(I_3, J_3, K_3) → poly3_3, k_3, i_3, j_3
  16. Polygon(I_4, J_4, K_4) → poly3_4, k_4, i_4, j_4
  17. Polygon(I_5, J_5, K_5) → poly3_5, k_5, i_5, j_5
  18. Polygon(I_6, J_6, K_6) → poly3_6, k_6, i_6, j_6
  19. Polygon(I_7, J_7, K_7) → poly3_7, k_7, i_7, j_7
  20. Polygon(I_8, J_8, K_8) → poly3_8, k_8, i_8, j_8
  21. Polygon(I_9, J_9, K_9) → poly3_9, k_9, i_9, j_9
  22. Polygon(L, M, N) → poly4, n, l, m
  23. Polygon(L_1, M_1, N_1) → poly4_1, n_1, l_1, m_1
  24. Polygon(L_2, M_2, N_2) → poly4_2, n_2, l_2, m_2
  25. Polygon(L_3, M_3, N_3) → poly4_3, n_3, l_3, m_3
  26. Polygon(L_4, M_4, N_4) → poly4_4, n_4, l_4, m_4
  27. Polygon(L_5, M_5, N_5) → poly4_5, n_5, l_5, m_5
  28. Polygon(L_6, M_6, N_6) → poly4_6, n_6, l_6, m_6
  29. Polygon(L_7, M_7, N_7) → poly4_7, n_7, l_7, m_7
  30. Polygon(L_8, M_8, N_8) → poly4_8, n_8, l_8, m_8
  31. Polygon(L_9, M_9, N_9) → poly4_9, n_9, l_9, m_9
  32. Polygon(O, P, Q, R) → poly5, o, p, q, r
  33. Polygon(O_1, P_1, Q_1, R_1) → poly5_1, o_1, p_1, q_1, r_1
  34. Polygon(O_2, P_2, Q_2, R_2) → poly5_2, o_2, p_2, q_2, r_2
  35. Polygon(O_3, P_3, Q_3, R_3) → poly5_3, o_3, p_3, q_3, r_3
  36. Polygon(S, T, U) → poly6, u, s, t
  37. Polygon(S_1, T_1, U_1) → poly6_1, u_1, s_1, t_1
  38. Polygon(S_2, T_2, U_2) → poly6_2, u_2, s_2, t_2
  39. Polygon(S_3, T_3, U_3) → poly6_3, u_3, s_3, t_3
  40. Polygon(S_5, T_5, U_5) → poly6_5, u_5, s_5, t_5
  41. Polygon(V, W, Z) → poly7, z_1, v, w
  42. Polygon(V_1, W_1, Z_1) → poly7_1, z_2, v_1, w_1
  43. Polygon(V_2, W_2, Z_2) → poly7_2, z_3, v_2, w_2
  44. Polygon(V_3, W_3, Z_3) → poly7_3, z_4, v_3, w_3
  45. Polygon(V_5, W_5, Z_5) → poly7_5, z_6, v_5, w_5
  46. Polygon(A_1, B_1, C_1, D_1) → poly8, a_1, b_1, c_1, d_1
  47. Polygon(A_2, B_2, C_2, D_2) → poly8_1, a_2, b_2, c_2, d_2
  48. Polygon(A_3, B_3, C_3, D_3) → poly8_2, a_3, b_3, c_3, d_3
  49. Polygon(A_4, B_4, C_4, D_4) → poly8_3, a_4, b_4, c_4, d_4
  50. Polygon(O_4, P_4, Q_4) → poly9, q_4, o_4, p_4
  51. Polygon(R_4, A_5, B_5) → poly10, b_5, r_4, a_5
  52. Polygon(O_5, P_5, Q_5) → poly9_1, q_5, o_5, p_5
  53. Polygon(R_5, A_6, B_6) → poly10_1, b_6, r_5, a_6
  54. Polygon(O_6, P_6, Q_6) → poly9_2, q_6, o_6, p_6
  55. Polygon(R_6, A_7, B_7) → poly10_2, b_7, r_6, a_7
  56. Polygon(O_7, P_7, Q_7) → poly9_3, q_7, o_7, p_7
  57. Polygon(R_7, A_8, B_8) → poly10_3, b_8, r_7, a_8
  58. Polygon(O_8, P_8, Q_8) → poly9_4, q_8, o_8, p_8
  59. Polygon(R_8, A_9, B_9) → poly10_4, b_9, r_8, a_9
  60. Polygon(O_9, P_9, Q_9) → poly9_5, q_9, o_9, p_9
  61. Polygon(R_9, A_{10}, B_{10}) → poly10_5, b_{10}, r_9, a_{10}
  62. Polygon(O_{10}, P_{10}, Q_{10}) → poly9_6, q_{10}, o_{10}, p_{10}
  63. Polygon(R_{10}, A_{11}, B_{11}) → poly10_6, b_{11}, r_{10}, a_{11}
  64. Polygon(O_{11}, P_{11}, Q_{11}) → poly9_7, q_{11}, o_{11}, p_{11}
  65. Polygon(R_{11}, A_{12}, B_{12}) → poly10_7, b_{12}, r_{11}, a_{12}
  66. Polygon(O_{12}, P_{12}, Q_{12}) → poly9_8, q_{12}, o_{12}, p_{12}
  67. Polygon(R_{12}, A_{13}, B_{13}) → poly10_8, b_{13}, r_{12}, a_{13}
  68. Polygon(O_{13}, P_{13}, Q_{13}) → poly9_9, q_{13}, o_{13}, p_{13}
  69. Polygon(R_{13}, A_{14}, B_{14}) → poly10_9, b_{14}, r_{13}, a_{14}
  70. Polygon(C_5, D_5, C_6) → poly11, c_6, c_5, d_5
  71. Polygon(D_6, S_6, T_6) → poly12, t_6, d_6, s_6
  72. Polygon(C_7, D_7, C_8) → poly11_1, c_7, c_8, d_7
  73. Polygon(D_8, S_7, T_7) → poly12_1, t_7, d_8, s_7
  74. Polygon(C_9, D_9, C_{10}) → poly11_2, c_9, c_{10}, d_9
  75. Polygon(D_{10}, S_8, T_8) → poly12_2, t_8, d_{10}, s_8
  76. Polygon(C_{11}, D_{11}, C_{12}) → poly11_3, c_{11}, c_{12}, d_{11}
  77. Polygon(D_{12}, S_9, T_9) → poly12_3, t_9, d_{12}, s_9
  78. Polygon(C_{13}, D_{13}, C_{14}) → poly11_4, c_{13}, c_{14}, d_{13}
  79. Polygon(D_{14}, S_{10}, T_{10}) → poly12_4, t_{10}, d_{14}, s_{10}

AI Drawing Prompt Reference

Create a border tile pattern consisting of multiple squares and triangles. First, draw 9 squares, each with 4 vertices. Then, draw a smaller square in the center of each square. Next, draw a triangle in the center of each smaller square. Finally, draw 3 large triangles at the top-left, top-right, and bottom-right corners of the pattern.
The prompt above was compiled from the original drawing commands and is for reference only.