伊斯兰几何图案 by chris cambré (4)
几何画板及绘图内容加载中,请稍等……
这个范例演示了伊斯兰几何图案的构造方法。涉及的核心数学概念包括对称性、交点和几何作图。通过使用GeoGebra中的Point、CircleArc、Polygon、PolyLine、Segment、Intersect等命令,可以构造出复杂的几何图案。适合初中及以上学生或数学爱好者学习和探索。
GeoGebra 命令及参数
Point(xAxis) → HPoint(xAxis) → ICircleArc(G, H, I) → cPolygon(V_1, U_1, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, A_2, Z_1, W_1, B_2, C_2, D_2, Q_2, F_2, G_2, H_2) → veelhoek1, v_1, h_2, i_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, a_2, u_1, z_1, w_1, b_2, c_2, d_2, q_2, f_2, g_2Polygon(S_2, I, S_1, E_2, R_2, C_2) → veelhoek2, s_2, i, s_1, e_2, r_2, fPolygon(T_1, J, B_3, H_1, T_2, U_2, V_2, W_2, Z_2, G_2, A_3) → veelhoek3, t_1, a_3, b_3, j, h_1, t_2, u_2, v_2, w_2, z_2, gPolygon(Q_1, C_3, O, D_3, M_2, E_3, F_3, G_3, H_3, I_3, I_1) → veelhoek4, q_1, i_1, o, c_3, d_3, h, e_3, f_3, g_3, h_3, i_3Polygon(B_3, Q_2, E_2, L_3) → vierhoek1, k, l, m, l_3Polygon(O_2, C_3, K_3, J_3) → vierhoek2, n, p, k_3, j_3Polygon(I_2, W_2, O_3, P_3) → vierhoek3, q, r, o_3, p_3Polygon(F_3, K_2, N_3, M_3) → vierhoek4, s, t, n_3, m_3Polygon(O_3, Q_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, H_3, I_4, U_2, M_3, J_4, R_3, S_3, T_3, U_3, V_3, W_3, Z_3) → veelhoek5, d, z_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, f_1, q_3, i_4, g_1, j_4, e, r_3, s_3, t_3, u_3, v_3, w_3Polygon(U_3, F_1, E_1) → driehoek1, e_1, j_1, k_1Polygon(D_1, K_4, W_3, T_4, E_1, K, L, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4) → veelhoek6, d_1, s_4, l_1, t_4, m_1, k_5, l_5, k_4, l_4, m_4, n_4, o_4, p_4, q_4, r_4Polygon(B_1, A_1, V_4) → driehoek2, v_4, b_1, a_1Polygon(V_4, W_4, H_5, I_5, J_5, K_5, L_4, L_5, U_4, M_5, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5) → veelhoek7, n_1, g_5, h_5, i_5, j_5, p_1, r_1, c_1, u_4, m_5, w_4, z_4, a_5, b_5, c_5, d_5, e_5, f_5Polygon(A_1, W, N_5, O_5, P_5, Q_5, Z_4, R_5) → veelhoek8, n_5, w, p_5, o_5, q_5, r_5, s_5, t_5Polygon(N_5, S_5, U, T_5, U_5, V_5, V, W_5, Z_5, A_6) → veelhoek9, f_6, a_6, g_6, u, h_6, u_5, v_5, v, w_5, z_5Polygon(U_5, S, B_6, T) → vierhoek5, i_6, s_6, b_6, t_6Polygon(Q, P, R, B_6) → vierhoek6, q_6, p_6, r_6, j_6Polygon(O_1, C_6, B_5, D_6, P_5, E_6, Z_5, Z) → veelhoek10, o_1, c_6, k_6, d_6, l_6, e_6, m_6, z_6Polygon(P_1, D_5, O_1) → driehoek3, n_6, f_7, g_7Polygon(L_1, F_6, H_5, M_6, M_1, M, N, C_4, G_6, H_6, I_6, P_4, J_6, K_6, L_6) → veelhoek11, h_7, r_7, s_7, t_7, a_7, m_8, n_8, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7PolyLine(I, S_1, D_1, C_1, B_1, A_1, T_1, J, H_1, G_1, F_1, E_1, K, L) → b_7PolyLine(O_1, P_1, O, Q_1, R_1, H, N_1, M_1, M, N, L_1, K_1, J_1, I_1) → c_7PolyLine(A_1, W, O_1, U, S, Q, P, R, T, V, Z) → d_7Point(c) → N_6Polygon(H, N_6, A_2, O_6, J_3, R_1) → veelhoek12, h_8, e_7, f_8, o_6, g_8, i_8Point(c) → P_6Polygon(I, S_1, D_1, C_1, B_1, A_1, W, U, S, Q, P, R, T_1, T, V, Z, O_1, P_1, N_1, M_1, M, N, L_1, J, K_1, J_1, I_1, O, Q_1, R_1, H, N_6, P_6, S_2, H_1, G_1, F_1, E_1, K, L) → veelhoek13, j_8, b_8, c_8, d_8, e_8, f_9, g_9, h_9, i_9, j_9, k_9, k_8, l_9, m_9, n_9, p_9, q_9, r_9, s_9, t_9, a_9, b_9, l_8, c_9, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, p_8, m_{10}, q_8, r_8, s_8, t_8, a_8Segment(N_1, F_5) → n_{10}Segment(U_4, C_1) → p_{10}Segment(K_1, E_4) → q_{10}Polygon(K_1, E_4, L_1) → driehoek4, r_{10}, s_{10}, t_{10}Segment(L_1, E_4) → a_{10}Polygon(I_1, G_4, J_1) → driehoek5, b_{10}, c_{10}, d_{10}Polygon(G_1, S_3, H_1) → driehoek6, e_{10}, f_{11}, g_{11}Polygon(M_1, F_5, N_1) → driehoek7, h_{11}, i_{11}, j_{11}Polygon(D_1, C_1, U_4) → driehoek8, k_{11}, l_{11}, m_{11}Intersect(c, k_{10}, 2) → Q_6Point(xAxis) → R_6Point(xAxis) → B_7Polygon(Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7) → veelhoek14, n_{11}, a_{11}, p_{11}, q_{11}, r_{11}, u_6, v_6, w_6, s_{11}, t_{11}Point(b_7) → C_7Segment(T_6, C_7) → b_{11}Point(k_8) → D_7Segment(S_6, D_7) → c_{11}Point(h_{10}) → E_7Segment(Z_6, E_7) → d_{11}Point(h_{10}) → F_7Segment(A_7, F_7) → e_{11}Polygon(G_7, H_7, Q_7, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7) → veelhoek15, f_{12}, n_{12}, b_{13}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, o_7Segment(Q_7, W_6) → q_{12}Segment(H_7, U_6) → r_{12}Point(h_7) → R_7Point(s_9) → W_7PolyLine(R_7, N_7, M_7, S_7, T_7, U_7, V_7, W_7) → p_{12}Point(j_1) → Z_7Point(b_7) → C_8PolyLine(Z_7, K_7, L_7, S_7, T_7, A_8, B_8, C_8) → s_{12}PolyLine(B_8, D_8, E_8, F_8, G_8, H_8, V_7, U_7, A_8) → t_{12}Point(f_7) → I_8Point(n_9) → K_8PolyLine(I_8, G_8, F_8, J_8, K_8) → a_{12}Point(v_4) → L_8Point(g_9) → M_8PolyLine(L_8, E_8, F_8, J_8, M_8) → b_{12}Point(m_9) → N_8Point(h_9) → O_8Segment(N_8, O_8) → c_{12}
AI 绘图提示语参考
绘制一个基于伊斯兰几何图案的复杂对称图形。首先在水平轴上取两个点,并构造一段圆弧。随后,通过一系列多边形(包括三角形、四边形和更多边的多边形)围绕圆弧和轴心排列,形成星形与花瓣状的交错图案。这些多边形相互连接、嵌套,并沿对称轴分布。接着,用折线勾勒出图案的轮廓骨架,并在圆弧上取点,连接这些点与多边形顶点,形成内部细分的几何结构。最后,在轴线上添加新点,并构造一个包含这些点的大多边形,同时从折线和多边形上取点,用线段连接,完善整个图案的对称与层次感。
以上提示语为根据原始绘图命令整理而来,仅供参考。