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Kharraqan 1 Islamic Geometric Patterns

Kharraqan 1 Islamic Geometric Patterns
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2019-12-31 21:50
CirclePolygonOptimizationGeometric Construction
This example demonstrates the construction of Islamic geometric patterns, involving symmetry, geometric mean, reflection, and linear programming. It uses commands like Point and Polygon in GeoGebra. Suitable for high school and above mathematics learning and geometric construction teaching.

GeoGebra Commands & Parameters

  1. Point(xAxis) → H_6
  2. Polygon(O_5, N_5, V_5, U_5, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6) → veelhoek3, h, n_6, j, k, i, g_6, h_6, i_6, j_6, k_6, l_6, m_6
  3. Polygon(C_6, D_6, W_6, Z_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6) → veelhoek4, l, v_6, w_6, z_6, m, o_6, p_6, q_6, r_6, s_6, t_6, u_6
  4. Point(xAxis) → H_7
  5. Polygon(L_5, A_7, G_6, M_5, B_7, C_7, D_7, E_7, F_7, G_7, H_7, H_6) → veelhoek5, n, p, q, r, a_7, b_7, c_7, d_7, e_7, f_7, g_7, h_7
  6. Polygon(O_6, E_6, N_7, P_6, F_6, R_5, S_5, I_7, J_7, K_7, L_7, M_7) → veelhoek6, s, m_7, n_7, d, t, a, b, c, i_7, j_7, k_7, l_7
  7. Polygon(G_7, H_7, S_7, R_7, I_6, J_6, O_7, P_7, Q_7, T_7, U_7, V_7) → veelhoek7, e, v_7, s_7, r_7, f_1, g_1, h_1, o_7, p_7, q_7, t_7, u_7
  8. Polygon(I_7, T_5, F_8, J_7, O_4, W_7, Z_7, A_8, B_8, C_8, D_8, E_8) → veelhoek8, i_1, e_8, f_8, l_1, j_1, k_1, w_7, z_7, a_8, b_8, c_8, d_8
  9. Polygon(K_8, J_8, I_8, L_8, Z_7, W_7, J_5, K_5, A_7, B_7, G_8, H_8) → veelhoek9, k_8, h_8, i_8, l_8, j_8, m_1, n_1, p_1, q_1, r_1, s_1, g_8
  10. Polygon(N_8, Q_6, N_7, M_7, M_8, P_8, O_8) → veelhoek10, n_8, t_1, a_1, b_1, m_8, p_8, o_8
  11. Polygon(P_8, M_8, L_7, K_7, F_8, E_8, R_8, Q_8) → veelhoek11, c_1, d_1, e_1, f_2, g_2, h_2, r_8, q_8
  12. Polygon(V_8, H_8, G_8, C_7, D_7, S_8, T_8, U_8) → veelhoek12, v_8, i_2, j_2, k_2, l_2, s_8, t_8, u_8
  13. Polygon(T_8, S_8, E_7, F_7, R_7, S_7, W_8) → veelhoek13, m_2, n_2, p_2, q_2, r_2, s_2, w_8
  14. Polygon(B_9, A_9, B_8, A_8, J_8, K_8, Z_8) → veelhoek14, b_9, a_9, t_2, a_2, b_2, c_2, z_8
  15. Polygon(Q_5, F_6, U_5, R_1, E_6, D_6, C_6, B_6, A_6, Z_5, W_5, V_5) → veelhoek1, q_5, v_5, u_5, f, f_6, e_6, d_6, c_6, b_6, a_6, z_5, w_5
  16. Polygon(R_1, O_5, R_5, Q_5, N_5, M_5, L_5, K_5, J_5, O_4, T_5, S_5) → veelhoek2, g, s_5, r_5, d_2, o_5, n_5, m_5, l_5, k_5, j_5, o_4, t_5
  17. Polygon(A_4, W_6, Z_6, B_6, A_6, B_4) → veelhoek15, a_4, e_2, f_3, g_3, h_3, b_4
  18. Polygon(R_8, D_8, C_8, A_9) → vierhoek1, i_3, j_3, k_3, l_3
  19. Polygon(Z_8, L_8, I_8, V_8) → vierhoek2, m_3, n_3, p_3, q_3
  20. Polygon(B_4, F_3, M_6, N_6, W_5, Z_5) → veelhoek16, r_3, s_3, t_3, a_3, b_3, c_3
  21. Polygon(F_3, E_3, P_7, O_7, K_6, L_6) → veelhoek17, d_3, e_3, f_4, g_4, h_4, i_4

AI Drawing Prompt Reference

Draw an Islamic geometric pattern based on symmetry and geometric mean. Start with two points on the horizontal axis as anchors. Around these, construct multiple interlocking dodecagons and polygons that rotate and reflect to form star-like and petal-shaped grids. The pattern consists of several groups of polygons, each with twelve vertices, sharing edges or vertices to ensure precise boundary alignment. Use polygon tools to connect vertices sequentially, creating a complex yet regular geometric ornament suitable for demonstrating symmetry and transformations in mathematics education.
The prompt above was compiled from the original drawing commands and is for reference only.