Friday Mosque in Isfahan Northeast (2)

Friday Mosque in Isfahan Northeast (2)
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2020-04-30 20:07
This example demonstrates the geometric construction of the Friday Mosque in Isfahan Northeast. The core mathematical concepts involved include geometric construction and transformation. Using GeoGebra commands such as Segment, Mirror, Point, PolyLine, Polygon, and Intersect, the complex structure of the mosque can be constructed. Suitable for high school or university geometry courses.

GeoGebra Commands & Parameters

  1. Segment(Z_7, A_8) → d_2
  2. Mirror(T_7, d_2) → N_8
  3. Mirror(Q_7, d_2) → Q_8
  4. Mirror(U_7, d_2) → O_8
  5. Segment(N_8, O_8) → n
  6. Point(n) → V_8
  7. PolyLine(G_5, H_5, I_5, J_5) → d
  8. Point(d) → W_5
  9. PolyLine(U_3, A_4, J_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4) → a
  10. Point(a) → I_6
  11. PolyLine(U_3, V_3, S_4, T_4, K_4, L_4, M_4, N_4, O_4, P_4, Q_4, R_4) → b
  12. Point(b) → U_5
  13. PolyLine(R_1, S_1, D_2, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2) → m
  14. Point(m) → C_6
  15. Polygon(Q_5, R_5, C_6, D_6, E_6, F_6, G_6, H_6, I_6, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6) → veelhoek4, q_5, b_6, c_6, d_6, e_6, f_6, g_6, h_6, i_6, r_5, s_5, t_5, u_5, v_5, w_5, z_5, a_6
  16. Point(d_6) → L_7
  17. Polygon(E, F, G, H, I) → veelhoek1, e, f, g, h, i
  18. PolyLine(J, K, T, L, M, N, O, P, Q, R, S) → j
  19. Point(i) → A_1
  20. Point(h) → B_1
  21. PolyLine(G_1, H_1, Q_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1) → l
  22. PolyLine(U, V, F_1, W, Z, A_1, I, B_1, C_1, D_1, E_1) → k
  23. PolyLine(L_2, M_2, N_2, O_2, P_2) → p
  24. PolyLine(Q_2, R_2, S_2, T_2, U_2) → q
  25. Point(f) → G_3
  26. Point(f) → J_3
  27. Point(h) → O_3
  28. Polygon(Q_3, G_1, C_2, Q_1, S_1, I_1, U_1, K_1, W_1, M_1, A_2, O_1) → veelhoek2, q_3, o_1, c_2, q_1, g_1, s_1, i_1, u_1, k_1, w_1, m_1, a_2
  29. Polygon(R_3, S_3, T_3, M_5, N_5, W_3, Z_3) → veelhoek3, l_1, n_1, p_1, r_1, t_1, a_1, b_1
  30. PolyLine(D_5, E_5, T_3) → c
  31. PolyLine(A_5, F_5, B_5, C_5) → h_1
  32. PolyLine(K_5, L_5, W_3) → j_1
  33. PolyLine(J_6, K_6, L_6, M_6, N_6) → c_1
  34. Point(i) → O_6
  35. Point(h) → S_6
  36. PolyLine(V_6, W_2, I_3, U_6, K_3, L_3, M_3, N_3, O_3, P_5, I_2, W_6, O_5, B_3, C_3, D_3, E_3, F_3, T_6, H_3) → t
  37. PolyLine(E_2, F_2, W, G_2, A_1, U_4) → n_3
  38. PolyLine(Z_4, B_1, H_2, D_1, J_2, K_2) → f_1
  39. PolyLine(V_4, Q_6, W_4) → d_1
  40. PolyLine(V_2, W_2, A_3, B_3, U_4, V_4, H_3) → r
  41. PolyLine(Z_2, I_2, P_3, O_3, Z_4, W_4, I_3) → s
  42. Polygon(A_7, B_7, C_7, D_7, E_7, F_7) → veelhoek5, e_1, f_2, g_2, h_2, i_2, j_2
  43. Polygon(J_7, K_7, L_7, M_7, N_7, U_7) → veelhoek6, k_2, l_2, m_2, n_2, p_2, b_2
  44. Segment(H_7, Q_7) → q_2
  45. Segment(R_7, S_7) → r_2
  46. Segment(T_7, U_7) → s_2
  47. Point(d_6) → V_7
  48. Segment(V_7, W_7) → t_2
  49. Mirror(J_7, d_2) → B_8
  50. Mirror(K_7, d_2) → C_8
  51. Mirror(L_7, d_2) → D_8
  52. Mirror(M_7, d_2) → E_8
  53. Mirror(N_7, d_2) → F_8
  54. Mirror(U_7, d_2) → G_8
  55. Polygon(B_8, C_8, D_8, E_8, F_8, G_8) → veelhoek6', b_8, c_8, d_8, e_8, f_8, g_8
  56. Mirror(A_7, d_2) → H_8
  57. Mirror(B_7, d_2) → I_8
  58. Mirror(C_7, d_2) → J_8
  59. Mirror(D_7, d_2) → K_8
  60. Mirror(E_7, d_2) → L_8
  61. Mirror(F_7, d_2) → M_8
  62. Polygon(H_8, I_8, J_8, K_8, L_8, M_8) → veelhoek5', h_8, i_8, j_8, k_8, l_8, m_8
  63. Mirror(H_7, d_2) → P_8
  64. Segment(P_8, Q_8) → f_3
  65. Mirror(V_7, d_2) → R_8
  66. Mirror(W_7, d_2) → S_8
  67. Segment(R_8, S_8) → g_3
  68. Mirror(R_7, d_2) → T_8
  69. Mirror(S_7, d_2) → U_8
  70. Polygon(V_8, W_8, Q_8, Z_8, A_9, B_9) → veelhoek7, e_2, i_3, j_3, k_3, l_3, m_3
  71. Segment(T_8, U_8) → h_3
  72. Mirror(V_8, d_2) → C_9
  73. Mirror(W_8, d_2) → D_9
  74. Mirror(Q_8, d_2) → E_9
  75. Mirror(Z_8, d_2) → F_9
  76. Mirror(A_9, d_2) → G_9
  77. Mirror(B_9, d_2) → H_9
  78. Polygon(C_9, D_9, E_9, F_9, G_9, H_9) → veelhoek7', c_9, d_9, e_9, f_9, g_9, h_9
  79. Polygon(I_9, J_9, K_9, L_9, M_9, N_9, O_9) → veelhoek8, i_9, j_9, k_9, l_9, m_9, n_9, o_9
  80. Intersect(h, i) → P_9
  81. Segment(P_9, Q_9) → p_3
  82. Mirror(I_9, p_3) → R_9
  83. Mirror(J_9, p_3) → S_9
  84. Mirror(K_9, p_3) → T_9
  85. Mirror(L_9, p_3) → U_9
  86. Mirror(M_9, p_3) → V_9
  87. Mirror(N_9, p_3) → W_9
  88. Mirror(O_9, p_3) → Z_9
  89. Polygon(R_9, S_9, T_9, U_9, V_9, W_9, Z_9) → veelhoek8', r_9, s_9, t_9, u_9, v_9, w_9, z_9