伊斯兰几何图案的 GeoGebra 演示

伊斯兰几何图案的 GeoGebra 演示
几何画板及绘图内容加载中,请稍等……
2019-12-31 22:31
①本范例通过 GeoGebra 演示伊斯兰几何图案的构建过程,展示其复杂的对称性和分形结构;②涉及的核心数学概念包括对称性、多边形构造、几何变换和组合数学;③作图要点提炼自构造摘要,主要用到了 Polygon(多边形)、Segment(线段)、Intersect(交点)等 GeoGebra 命令及对象;④适合高中及以上数学学习者,用于理解几何作图、对称性原理及复杂图案的生成规律。

GeoGebra 命令及参数

  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