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Geogebra Demonstration of Islamic Geometric Patterns

Geogebra Demonstration of Islamic Geometric Patterns
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2019-12-31 22:31
PolygonGeometric Construction
This example demonstrates the construction of Islamic geometric patterns using GeoGebra, showcasing their intricate symmetry and fractal structures. The core mathematical concepts involved include symmetry, polygon construction, geometric transformations, and combinatorics. Key GeoGebra commands and objects used in the construction, as outlined in the summary, are Polygon, Segment, and Intersect. It is suitable for high school and above students to understand geometric constructions, symmetry principles, and the generation of complex patterns.

GeoGebra Commands & Parameters

  1. Polygon(C, D, 10) → veelhoek1, f, p, E, F, G, H, I, J, K, L, g, h, i, j, k, l, m, n
  2. Polygon(E, D, 10) → veelhoek2, q, f_1, M, N, O, P, Q, R, S, T, r, s, t, a, b, c, d, e
  3. Polygon(C, L, 10) → veelhoek3, g_1, q_1, U, V, W, Z, A_1, B_1, C_1, D_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1
  4. Polygon(N, C_1, 10) → veelhoek4, r_1, g_2, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, s_1, t_1, a_1, b_1, c_1, d_1, e_1, f_2
  5. Polygon(H, G, 10) → veelhoek5, h_2, r_2, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2
  6. Polygon(J, I, 10) → veelhoek6, s_2, h_3, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, t_2, a_2, b_2, c_2, d_2, e_2, f_3, g_3
  7. Polygon(V_1, S_1, 10) → veelhoek7, i_3, s_3, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3
  8. Polygon(H_2, G_2, 10) → veelhoek8, t_3, i_4, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, a_3, b_3, c_3, d_3, e_3, f_4, g_4, h_4
  9. Polygon(J_2, I_2, 10) → veelhoek9, j_4, t_4, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, k_4, l_4, m_4, n_4, p_4, q_4, r_4, s_4
  10. Polygon(J_2, E_3, F_3, Z_1, W_1, K_2) → veelhoek10, a_4, b_4, c_4, z_1, w_1, d_4
  11. Polygon(N_2, G_2, F_2, R_1, Q_1, G_3) → veelhoek11, e_4, f_5, g_5, h_5, i_5, j_5
  12. Polygon(S_1, V_1, U_1, I, H, T_1) → veelhoek12, k_5, v_1, u_1, i_6, h_6, l_5
  13. Polygon(J, D_2, H_3, U, L, K) → veelhoek13, j_6, m_5, n_5, u, l_6, k_6
  14. Polygon(M_1, G, F, E, T, I_3) → veelhoek14, p_5, g_6, f_6, e_5, t_5, q_5
  15. Polygon(D, C, D_1, C_1, N, M) → veelhoek15, d_5, c_5, r_5, s_5, n_6, m_6
  16. Segment(J_3, K_3) → a_5
  17. Segment(L_3, M_3) → b_5
  18. Segment(N_3, O_3) → p_6
  19. Segment(P_3, Q_3) → q_6
  20. Segment(R_3, S_3) → r_6
  21. Segment(O_3, T_3) → s_6
  22. Intersect(a_5, q_6) → U_3
  23. Intersect(a_5, r_6) → V_3
  24. Intersect(b_5, r_6) → W_3
  25. Intersect(b_5, q_6) → Z_3
  26. Polygon(U_3, V_3, W_3, Z_3) → vierhoek1, u_3, v_3, w_3, z_3
  27. Polygon(A_4, U_3, B_4, Z_3) → vierhoek2, t_6, a_6, b_6, c_6