MathPlotAI Logo MathPlotAI

Constructing Islamic Geometric Patterns

Constructing Islamic Geometric Patterns
Loading the math board and drawing, please wait…
2019-12-31 17:39
PolygonTrigonometryGeometric Construction
This example demonstrates the construction of Islamic geometric patterns, showing how basic shapes combine to form intricate decorative designs. Key math concepts include symmetry, polygon construction, equation solving, and geometric distribution. The construction uses GeoGebra commands like Segment, Point, Polygon, Intersect, and Line. Suitable for high school and above, it helps learners understand the mathematical principles behind geometric constructions and pattern design.

GeoGebra Commands & Parameters

  1. Segment(H_8, B_9) → p_{15}
  2. Point(p_{15}) → T_9
  3. Polygon(H_8, I_8, 4) → veelhoek27, m_{14}, n_{14}, p_{14}, q_{14}, G_8, J_8
  4. Intersect(m_{14}, q_{14}) → C_{10}
  5. Point(yAxis) → C
  6. Line(D, E) → f
  7. Point(f) → F
  8. Point(yAxis) → G
  9. Point(f) → H
  10. Point(xAxis) → I
  11. Polygon(G, H, I, J, C, F, K, L) → veelhoek1, g, h, i, j, c, f_1, k, l
  12. Point(xAxis) → O
  13. Polygon(L, K, F, M, N, O, P, Q) → veelhoek2, l_1, k_1, f_2, m, n, o, p, q
  14. Point(xAxis) → T
  15. Polygon(H, R, S, T, U, V, J, I) → veelhoek3, h_1, r, s, t, u, v, j_1, i_1
  16. Polygon(U, W, Z, A_1, B_1, C_1, J, V) → veelhoek4, u_1, w, z_1, a_1, b_1, c_1, j_2, v_1
  17. Point(yAxis) → D_1
  18. Polygon(F, C, J, C_1, B_1, D_1, E_1, F_1) → veelhoek5, f_3, c_2, j_3, a, b, d_1, e_1, d
  19. Polygon(N, M, F, F_1, E_1, G_1, H_1, I_1) → veelhoek6, n_1, m_1, f_4, e, g_1, p_1, q_1, r_1
  20. Polygon(J_1, P, O, N, K_1) → veelhoek7, s_1, p_2, o_1, n_2, t_1
  21. Polygon(K_1, N, I_1, H_1, L_1) → veelhoek8, g_2, n_3, h_2, i_2, k_2
  22. Polygon(S, M_1, N_1, U, T) → veelhoek9, s_2, l_2, m_2, u_2, t_2
  23. Point(yAxis) → Q_1
  24. Polygon(H, G, L, O_1, P_1, Q_1, R_1, S_1) → veelhoek10, h_3, g_3, l_3, q_2, r_2, a_2, b_2, d_2
  25. Polygon(P_1, O_1, L, Q, P, T_1, U_1, V_1) → veelhoek11, e_2, i_3, l_4, q_3, p_3, k_3, m_3, r_3
  26. Polygon(W_1, U_1, T_1, P, J_1) → veelhoek12, w_1, s_3, t_3, p_4, a_3
  27. Polygon(A_2, Z_1, S, R, H, S_1, R_1, B_2) → veelhoek13, b_3, c_3, s_4, r_4, h_4, d_3, e_3, g_4
  28. Polygon(C_2, M_1, S, Z_1, A_2) → veelhoek14, i_4, j_4, s_5, k_4, m_4
  29. Polygon(D_2, Z, W, U, N_1) → veelhoek15, n_4, z_2, w_2, u_3, q_4
  30. Polygon(F_2, E_2, Z, D_2) → vierhoek1, t_4, a_4, z_3, b_4
  31. Polygon(E_2, G_2, B_1, A_1, Z) → veelhoek16, c_4, d_4, e_4, f_5, z_4
  32. Polygon(G_2, H_2, E_1, D_1, B_1) → veelhoek17, g_5, h_5, i_5, j_5, k_5
  33. Polygon(H_2, I_2, H_1, G_1, E_1) → veelhoek18, l_5, m_5, n_5, p_5, q_5
  34. Polygon(I_2, J_2, L_1, H_1) → vierhoek2, r_5, t_5, a_5, b_5
  35. Point(yAxis) → K_2
  36. Point(yAxis) → P_3
  37. Polygon(K_2, L_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, M_2, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, N_2, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, O_2, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, P_2, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, Q_2, R_2, S_2, T_2) → veelhoek19, c_5, k_6, l_6, v_2, m_6, n_6, p_6, q_6, r_6, s_6, t_6, d_5, a_6, b_6, c_6, d_6, e_6, f_7, g_7, h_7, i_7, o_3, e_5, j_7, k_7, l_7, m_7, n_7, p_7, v_3, w_3, q_7, r_7, f_6, s_7, t_7, a_7, b_7, c_7, d_7, e_7, f_8, g_8, h_8, o_2, i_8, j_8, k_8, o_4, l_8, m_8, n_8, p_8, g_6, h_6, i_6, j_6
  38. Point(t_6) → T_4
  39. Polygon(T_4, B_3, A_3, F_3) → vierhoek3, q_8, r_8, s_8, t_8
  40. Polygon(Z_2, W_2, U_4, Q_2, P_2) → veelhoek20, a_8, b_8, c_8, d_8, e_8
  41. Point(yAxis) → V_4
  42. Polygon(O_2, N_2, V_4, Q_4, P_4) → veelhoek21, f_9, g_9, v_4, h_9, i_9
  43. Polygon(O_4, W_4, I_4) → driehoek1, j_9, k_9, w_4
  44. Polygon(G_4, F_4, Z_4, B_4) → vierhoek4, l_9, m_9, n_9, p_9
  45. Point(xAxis) → A_5
  46. Point(xAxis) → V_5
  47. Polygon(L_3, K_3, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, A_5, S_5, T_5, U_5, V_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → veelhoek22, q_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, o_5, m_{10}, n_{10}, r_9, p_{10}, q_{10}, r_{10}, u_5, v_5, s_9, t_9, a_9, b_9, c_9, d_9, e_9
  48. Point(xAxis) → W_5
  49. Point(yAxis) → H_6
  50. Point(yAxis) → I_6
  51. Point(yAxis) → M_6
  52. Point(yAxis) → N_6
  53. Point(xAxis) → P_6
  54. Polygon(O_3, N_3, N_5, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, W_5, M_6, N_6, O_6, P_6, Z_5, T_5, S_5, A_6, B_6, C_6, O_5) → veelhoek23, s_{10}, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, t_{10}, q_{11}, r_{11}, s_{11}, o_6, t_{11}, w_5, z_5, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}
  55. Point(xAxis) → J_7
  56. Polygon(R_3, Q_3, H_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, Q_6, G_7, H_7, I_7, J_7, R_6, N_6, M_6, S_6, T_6, U_6, I_6) → veelhoek24, a_{11}, i_{12}, j_{12}, v_6, w_6, z_6, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, b_{11}, q_{12}, r_{12}, s_{12}, t_{12}, a_{12}, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, u_6
  57. Point(xAxis) → D_8
  58. Point(xAxis) → E_8
  59. Polygon(U_3, T_3, B_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, Z_7, E_8, A_8, B_8, C_8, D_8, L_7, H_7, G_7, M_7, N_7, O_7, C_7) → veelhoek25, b_{12}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, u_7, v_7, w_7, c_{12}, z_7, r_{13}, s_{13}, t_{13}, a_{13}, d_{12}, e_{12}, f_{13}, g_{13}, h_{13}, i_{13}, o_7
  60. Polygon(I_3, W_3, K_7, F_8, R_7, Q_7, Z_6, W_6, F_6, E_6, L_5) → veelhoek26, b_{13}, k_{14}, l_{14}, c_{13}, d_{13}, e_{13}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}
  61. Polygon(M_8, N_8, 4) → veelhoek28, r_{14}, s_{14}, t_{14}, a_{14}, O_8, P_8
  62. Segment(I_8, K_8) → b_{14}
  63. Segment(K_8, L_8) → c_{14}
  64. Segment(K_8, M_8) → d_{14}
  65. Segment(G_8, K_8) → e_{14}
  66. Segment(K_8, P_8) → f_{15}
  67. Segment(I_8, L_8) → g_{15}
  68. Segment(L_8, M_8) → h_{15}
  69. Polygon(U_8, V_8, 4) → veelhoek29, i_{15}, j_{15}, k_{15}, l_{15}, W_8, Z_8
  70. Segment(W_8, B_9) → m_{15}
  71. Segment(B_9, J_8) → n_{15}
  72. Segment(B_9, V_8) → q_{15}
  73. Segment(V_8, A_9) → r_{15}
  74. Segment(H_8, A_9) → s_{15}
  75. Segment(A_9, B_9) → t_{15}
  76. Polygon(E_9, F_9, 4) → veelhoek30, a_{15}, b_{15}, c_{15}, d_{15}, G_9, H_9
  77. Segment(N_8, C_9) → e_{15}
  78. Segment(O_8, C_9) → f_{16}
  79. Segment(C_9, E_9) → g_{16}
  80. Segment(C_9, F_9) → h_{16}
  81. Segment(F_9, D_9) → i_{16}
  82. Segment(D_9, N_8) → j_{16}
  83. Segment(C_9, D_9) → k_{16}
  84. Segment(J_8, R_8) → l_{16}
  85. Segment(Q_8, R_8) → m_{16}
  86. Segment(I_9, R_8) → n_{16}
  87. Segment(Q_8, I_9) → p_{16}
  88. Segment(I_9, J_9) → q_{16}
  89. Segment(R_8, J_9) → r_{16}
  90. Segment(Q_8, J_8) → s_{16}
  91. Segment(R_8, G_8) → t_{16}
  92. Segment(S_8, O_8) → a_{16}
  93. Segment(P_8, S_8) → b_{16}
  94. Segment(O_8, T_8) → c_{16}
  95. Segment(S_8, T_8) → d_{16}
  96. Segment(T_8, K_9) → e_{16}
  97. Segment(K_9, L_9) → f_{17}
  98. Segment(L_9, S_8) → g_{17}
  99. Polygon(M_9, N_9, O_9, P_9, Q_9, R_9, C_{10}, S_9, T_9) → veelhoek31, i_{17}, j_{17}, k_{17}, l_{17}, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}
  100. Segment(S_8, K_9) → h_{17}
  101. Point(s_{16}) → Z_9
  102. Intersect(p_{14}, q_{14}) → A_{10}
  103. Point(n_{15}) → B_{10}
  104. Polygon(B_{10}, M_9, N_9, U_9, V_9, W_9, Z_9, A_{10}) → veelhoek32, s_{17}, t_{17}, a_{17}, u_9, v_9, w_9, z_9, b_{17}
  105. Point(t_{16}) → D_{10}
  106. Point(p_{14}) → E_{10}
  107. Point(e_{14}) → H_{10}
  108. Polygon(E_{10}, D_{10}, V_9, U_9, F_{10}, G_{10}, H_{10}) → veelhoek33, c_{17}, d_{17}, e_{17}, f_{18}, g_{18}, h_{18}, i_{18}
  109. Point(b_{14}) → I_{10}
  110. Point(g_{15}) → J_{10}
  111. Intersect(m_{14}, n_{14}) → K_{10}
  112. Polygon(J_{10}, I_{10}, G_{10}, F_{10}, O_9, P_9, L_{10}, K_{10}) → veelhoek34, j_{18}, k_{18}, l_{18}, m_{18}, o_9, n_{18}, p_{18}, q_{18}
  113. Polygon(O_9, F_{10}, U_9, N_9) → vierhoek5, r_{18}, s_{18}, t_{18}, a_{18}
  114. Point(e_{14}) → M_{10}
  115. Point(b_{14}) → P_{10}
  116. Point(d_{14}) → Q_{10}
  117. Point(f_{15}) → R_{10}
  118. Intersect(b_{14}, c_{14}) → S_{10}
  119. Intersect(c_{14}, g_{15}) → T_{10}
  120. Point(g_{15}) → U_{10}
  121. Point(h_{15}) → V_{10}
  122. Polygon(U_{10}, N_{10}, O_{10}, V_{10}, T_{10}) → veelhoek36, u_{10}, h_{19}, i_{19}, v_{10}, j_{19}
  123. Intersect(h_{19}, i_{19}) → W_{10}
  124. Point(d_{14}) → Z_{10}
  125. Point(f_{15}) → A_{11}
  126. Intersect(b_{14}, e_{14}) → B_{11}
  127. Point(e_{14}) → C_{11}
  128. Point(b_{14}) → D_{11}
  129. Intersect(u_{10}, h_{19}) → E_{11}
  130. Polygon(W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}) → veelhoek35, w_{10}, z_{10}, b_{18}, c_{18}, d_{18}, e_{18}, f_{19}
  131. Point(h_{15}) → F_{11}
  132. Point(d_{14}) → G_{11}
  133. Intersect(r_{14}, a_{14}) → M_{11}
  134. Polygon(F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}) → veelhoek37, g_{19}, k_{19}, l_{19}, m_{19}, n_{19}, p_{19}, q_{19}, r_{19}
  135. Point(e_{15}) → R_{11}
  136. Point(j_{16}) → S_{11}
  137. Intersect(e_{15}, j_{16}) → T_{11}
  138. Polygon(N_{11}, O_{11}, K_{11}, J_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}) → veelhoek38, s_{19}, o_{11}, t_{19}, a_{19}, b_{19}, c_{19}, d_{19}, e_{19}, f_{20}
  139. Point(f_{15}) → U_{11}
  140. Point(b_{16}) → Z_{11}
  141. Point(b_{16}) → A_{12}
  142. Polygon(A_{12}, U_{11}, H_{11}, I_{11}, V_{11}, W_{11}, Z_{11}) → veelhoek39, g_{20}, u_{11}, h_{20}, i_{20}, v_{11}, w_{11}, z_{11}
  143. Point(c_{16}) → C_{12}
  144. Intersect(a_{16}, c_{16}) → D_{12}
  145. Point(f_{16}) → E_{12}
  146. Polygon(D_{12}, C_{12}, B_{12}, W_{11}, V_{11}, P_{11}, Q_{11}, E_{12}) → veelhoek40, j_{20}, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, q_{20}, r_{20}
  147. Polygon(V_{11}, I_{11}, J_{11}, P_{11}) → vierhoek6, s_{20}, t_{20}, a_{20}, b_{20}
  148. Intersect(e_{14}, h_{18}) → F_{12}
  149. Intersect(g_{18}, h_{18}) → G_{12}
  150. Intersect(b_{14}, j_{18}) → H_{12}
  151. Point(b_{14}) → I_{12}
  152. Point(e_{14}) → J_{12}
  153. Polygon(F_{12}, G_{12}, H_{12}, I_{12}, J_{12}) → veelhoek41, c_{20}, d_{20}, e_{20}, f_{21}, g_{21}
  154. Intersect(g_{15}, j_{18}) → K_{12}
  155. Intersect(g_{15}, u_{10}) → L_{12}
  156. Intersect(u_{10}, h_{19}) → M_{12}
  157. Intersect(h_{19}, i_{19}) → N_{12}
  158. Intersect(h_{15}, i_{19}) → O_{12}
  159. Intersect(h_{15}, g_{19}) → P_{12}
  160. Intersect(d_{14}, g_{19}) → Q_{12}
  161. Intersect(d_{14}, w_{10}) → R_{12}
  162. Point(f_{15}) → S_{12}
  163. Intersect(f_{15}, g_{20}) → T_{12}
  164. Point(u_{11}) → U_{12}
  165. Polygon(K_{12}, L_{12}, M_{12}, I_{12}, H_{12}) → veelhoek42, h_{21}, i_{21}, j_{21}, k_{21}, l_{21}
  166. Polygon(N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}) → veelhoek43, m_{21}, o_{12}, n_{21}, p_{21}, q_{21}
  167. Polygon(Q_{12}, U_{12}, T_{12}, S_{12}, R_{12}) → veelhoek44, r_{21}, u_{12}, s_{21}, t_{21}, a_{21}
  168. Polygon(V_{12}, W_{12}, Z_{12}, A_{13}) → vierhoek7, v_{12}, w_{12}, z_{12}, b_{21}