GeoGebra几何作图与函数图像示例
几何画板及绘图内容加载中,请稍等……
该范例演示了如何通过GeoGebra工具绘制几何图形和函数图像。核心数学概念包括几何变换、函数图像与坐标系。作图要点涉及使用Circle、Segment、Sequence等命令构建图形,并利用If和Random进行动态调整。适合初中生或高中生用于学习几何与函数的基础知识,以及理解图形变换的原理。
GeoGebra 命令及参数
Circle(A, 0.125) → fCircle(B, 0.125) → gCircle(C, 0.125) → hCircle(D, 0.125) → kCircle(E, 0.125) → pCircle(F, 0.125) → qCircle(G, 0.125) → rCircle(H, 0.125) → sCircle(I, 0.125) → tCircle(J, 0.125) → c_1Circle(K, 0.125) → d_1Circle(L, 0.125) → e_1Circle(M, 0.125) → f_1Circle(N, 0.125) → g_1Circle(O, 0.125) → h_1Circle(P, 0.125) → k_1Circle(Q, 0.125) → p_1Circle(R, 0.125) → q_1Circle(S, 0.125) → r_1Circle(T, 0.125) → s_1Segment(U, G_1) → iSegment(V, H_1) → jSegment(W, I_1) → lSegment(Z, J_1) → mSegment(A_1, K_1) → nSegment(B_1, N_1) → i_1Segment(C_1, L_1) → j_1Segment(D_1, M_1) → l_1Segment(E_1, P_1) → m_1Segment(F_1, O_1) → n_1Segment(G_1, D_2) → t_1Segment(G_1, C_2) → a_1Segment(E_2, H_1) → b_1Segment(H_1, V_2) → f_2Segment(F_2, I_1) → g_2Segment(I_1, U_2) → h_2Segment(G_2, J_1) → i_2Segment(J_1, T_2) → j_2Segment(H_2, K_1) → k_2Segment(K_1, S_2) → l_2Segment(I_2, N_1) → m_2Segment(N_1, R_2) → n_2Segment(J_2, L_1) → p_2Segment(L_1, Q_2) → q_2Segment(K_2, M_1) → r_2Segment(M_1, P_2) → s_2Segment(L_2, P_1) → t_2Segment(P_1, O_2) → a_2Segment(M_2, O_1) → b_2Segment(O_1, N_2) → c_2Segment(R_3, Q_1) → d_2Segment(W_2, Q_1) → e_2Segment(Q_3, R_1) → f_3Segment(Z_2, R_1) → g_3Segment(P_3, S_1) → h_3Segment(A_3, S_1) → i_3Segment(O_3, T_1) → j_3Segment(B_3, T_1) → k_3Segment(N_3, U_1) → l_3Segment(C_3, U_1) → m_3Segment(M_3, V_1) → n_3Segment(D_3, V_1) → p_3Segment(L_3, W_1) → q_3Segment(E_3, W_1) → r_3Segment(K_3, Z_1) → s_3Segment(F_3, Z_1) → t_3Segment(J_3, A_2) → a_3Segment(G_3, A_2) → b_3Segment(H_3, B_2) → c_3Segment(I_3, B_2) → d_3Segment(U_5, K_5) → e_3Segment(Q_6, K_5) → f_4Segment(V_5, L_5) → g_4Segment(P_6, L_5) → h_4Segment(W_5, M_5) → i_4Segment(O_6, M_5) → j_4Segment(Z_5, N_5) → k_4Segment(N_6, N_5) → l_4Segment(A_6, O_5) → m_4Segment(M_6, O_5) → n_4Segment(B_6, P_5) → p_4Segment(L_6, P_5) → q_4Segment(C_6, Q_5) → r_4Segment(J_6, Q_5) → s_4Segment(D_6, R_5) → t_4Segment(I_6, R_5) → a_4Segment(E_6, S_5) → b_4Segment(H_6, S_5) → c_4Segment(F_6, T_5) → d_4Segment(G_6, T_5) → e_4Segment(D_4, N_4) → f_5Segment(M_4, C_4) → g_5Segment(B_4, L_4) → h_5Segment(K_4, A_4) → i_5Segment(Z_3, J_4) → j_5Segment(I_4, W_3) → k_5Segment(V_3, H_4) → l_5Segment(G_4, U_3) → m_5Segment(T_3, F_4) → n_5Segment(E_4, S_3) → p_5Segment(O_4, E_4) → q_5Segment(E_4, J_5) → r_5Segment(P_4, F_4) → s_5Segment(F_4, I_5) → t_5Segment(Q_4, G_4) → a_5Segment(G_4, H_5) → b_5Segment(R_4, H_4) → c_5Segment(H_4, G_5) → d_5Segment(S_4, I_4) → e_5Segment(I_4, F_5) → f_6Segment(T_4, J_4) → g_6Segment(J_4, E_5) → h_6Segment(U_4, K_4) → i_6Segment(K_4, D_5) → j_6Segment(V_4, L_4) → k_6Segment(L_4, C_5) → l_6Segment(W_4, M_4) → m_6Segment(M_4, B_5) → n_6Segment(Z_4, N_4) → p_6Segment(N_4, A_5) → q_6Sort(Sequence[(random(), Element[DataList, k]), k, 1, Length[DataList]]) → RandomDataPairSequence(y(Element[RandomDataPair, k]), k, 1, e) → ChoosedListPolygon(R_6, D_7, E_7, O_7) → q1, r_6, d_7, e_7, o_7Polygon(D_7, S_6, N_7, E_7) → q2, s_6, t_6, n_7, a_6Polygon(S_6, C_7, F_7, N_7) → q3, b_6, c_7, f_7, c_6Polygon(C_7, T_6, M_7, F_7) → q4, d_6, e_6, m_7, g_7Polygon(T_6, B_7, G_7, M_7) → q5, h_7, b_7, i_7, j_7Polygon(B_7, U_6, L_7, G_7) → q6, k_7, u_6, l_7, p_7Polygon(U_6, A_7, H_7, L_7) → q7, q_7, a_7, r_7, s_7Polygon(A_7, V_6, K_7, H_7) → q8, t_7, v_6, f_8, g_8Polygon(V_6, Z_6, I_7, K_7) → q9, h_8, z_6, i_8, j_8Polygon(Z_6, W_6, J_7, I_7) → q10, k_8, w_6, l_8, m_8Polygon(E_7, O_7, P_7, B_8) → q11, n_8, p_8, q_8, b_8Polygon(E_7, N_7, Q_7, B_8) → q12, r_8, s_8, t_8, a_8Polygon(N_7, Q_7, A_8, F_7) → q13, c_8, d_8, e_8, f_9Polygon(F_7, A_8, R_7, M_7) → q14, g_9, h_9, i_9, j_9Polygon(M_7, G_7, Z_7, R_7) → q15, k_9, l_9, z_7, m_9Polygon(G_7, Z_7, S_7, L_7) → q16, n_9, p_9, q_9, r_9Polygon(L_7, S_7, W_7, H_7) → q17, s_9, t_9, w_7, a_9Polygon(H_7, K_7, T_7, W_7) → q18, b_9, c_9, d_9, e_9Polygon(K_7, I_7, V_7, T_7) → q19, f_{10}, g_{10}, v_7, h_{10}Polygon(I_7, J_7, U_7, V_7) → q20, i_{10}, j_{10}, u_7, k_{10}Segment(R_6, W_6) → l_{10}Segment(W_6, U_7) → m_{10}Segment(U_7, P_7) → n_{10}Segment(P_7, R_6) → p_{10}Segment(B_7, Z_7) → q_{10}Segment(O_7, J_7) → r_{10}Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair1Sequence(y(Element[RandomDataPair1, k]), k, 1, o) → Stratified1Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair2Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair3Sort(Sequence[(random(), Element[DataList1, k]), k, 1, Length[DataList1]]) → RandomDataPair4Sequence(y(Element[RandomDataPair2, k]), k, 1, o) → Stratified2Sequence(y(Element[RandomDataPair3, k]), k, 1, o) → Stratified3Sequence(y(Element[RandomDataPair4, k]), k, 1, o) → Stratified4Polygon(R_6, O_7, E_7, D_7) → q21, s_{10}, t_{10}, a_{10}, b_{10}Polygon(D_7, S_6, N_7, E_7) → q22, c_{10}, d_{10}, e_{10}, f_{11}Polygon(S_6, C_7, F_7, N_7) → q23, g_{11}, h_{11}, i_{11}, j_{11}Polygon(C_7, T_6, M_7, F_7) → q24, k_{11}, l_{11}, m_{11}, n_{11}Polygon(T_6, B_7, G_7, M_7) → q25, p_{11}, q_{11}, r_{11}, s_{11}Polygon(B_7, U_6, L_7, G_7) → q26, t_{11}, a_{11}, b_{11}, c_{11}Polygon(U_6, A_7, H_7, L_7) → q27, d_{11}, e_{11}, f_{12}, g_{12}Polygon(A_7, V_6, K_7, H_7) → q28, h_{12}, i_{12}, j_{12}, k_{12}Polygon(V_6, Z_6, I_7, K_7) → q29, l_{12}, m_{12}, n_{12}, p_{12}Polygon(Z_6, W_6, J_7, I_7) → q30, q_{12}, r_{12}, s_{12}, t_{12}Polygon(O_7, E_7, B_8, P_7) → q31, a_{12}, b_{12}, c_{12}, d_{12}Polygon(E_7, N_7, Q_7, B_8) → q32, e_{12}, f_{13}, g_{13}, h_{13}Polygon(N_7, F_7, A_8, Q_7) → q33, i_{13}, j_{13}, k_{13}, l_{13}Polygon(F_7, M_7, R_7, A_8) → q34, m_{13}, n_{13}, p_{13}, q_{13}Polygon(M_7, G_7, Z_7, R_7) → q35, r_{13}, s_{13}, t_{13}, a_{13}Polygon(G_7, L_7, S_7, Z_7) → q36, b_{13}, c_{13}, d_{13}, e_{13}Polygon(L_7, H_7, W_7, S_7) → q37, f_{14}, g_{14}, h_{14}, i_{14}Polygon(H_7, K_7, T_7, W_7) → q38, j_{14}, k_{14}, l_{14}, m_{14}Polygon(K_7, I_7, V_7, T_7) → q39, n_{14}, p_{14}, q_{14}, r_{14}Polygon(I_7, J_7, U_7, V_7) → q40, s_{14}, t_{14}, a_{14}, b_{14}If(o ≟ 4, strat1, o ≟ 8, Join[{strat1, strat2}], o ≟ 12, Join[{strat1, strat2, strat3}], o ≟ 16, Join[{strat1, strat2, strat3, strat4}]) → stratSort(Sequence[(random(), Element[DataList2, k]), k, 1, Length[DataList2]]) → RandomDataPair5Sequence(y(Element[RandomDataPair5, k]), k, 1, u / 5) → clusterPolygon(R_6, B_7, G_7, O_7) → q41, c_{14}, d_{14}, e_{14}, f_{15}Polygon(B_7, W_6, J_7, G_7) → q42, g_{15}, h_{15}, i_{15}, j_{15}Polygon(O_7, P_7, Z_7, G_7) → q43, k_{15}, l_{15}, m_{15}, n_{15}Polygon(G_7, Z_7, U_7, J_7) → q44, p_{15}, q_{15}, r_{15}, s_{15}Random(1, floor(20 / v)) → wIf(v ≟ 8, 2, round(20 / v)) → o_1Sequence(w + (k * o_1), k, 0, v - 1) → systemPolygon(R_6, D_7, E_7, O_7) → q45, t_{15}, a_{15}, b_{15}, c_{15}Polygon(D_7, S_6, N_7, E_7) → q46, d_{15}, e_{15}, f_{16}, g_{16}Polygon(S_6, C_7, F_7, N_7) → q47, h_{16}, i_{16}, j_{16}, k_{16}Polygon(C_7, T_6, M_7, F_7) → q48, l_{16}, m_{16}, n_{16}, p_{16}Polygon(T_6, B_7, G_7, M_7) → q49, q_{16}, r_{16}, s_{16}, t_{16}Polygon(B_7, U_6, L_7, G_7) → q50, a_{16}, b_{16}, c_{16}, d_{16}Polygon(U_6, A_7, H_7, L_7) → q51, e_{16}, f_{17}, g_{17}, h_{17}Polygon(A_7, V_6, K_7, H_7) → q52, i_{17}, j_{17}, k_{17}, l_{17}Polygon(V_6, Z_6, I_7, K_7) → q53, m_{17}, n_{17}, p_{17}, q_{17}Polygon(Z_6, W_6, J_7, I_7) → q54, r_{17}, s_{17}, t_{17}, a_{17}Polygon(O_7, E_7, B_8, P_7) → q55, b_{17}, c_{17}, d_{17}, e_{17}Polygon(E_7, N_7, Q_7, B_8) → q56, f_{18}, g_{18}, h_{18}, i_{18}Polygon(N_7, F_7, A_8, Q_7) → q57, j_{18}, k_{18}, l_{18}, m_{18}Polygon(F_7, M_7, R_7, A_8) → q58, n_{18}, p_{18}, q_{18}, r_{18}Polygon(M_7, G_7, Z_7, R_7) → q59, s_{18}, t_{18}, a_{18}, b_{18}Polygon(G_7, L_7, S_7, Z_7) → q60, c_{18}, d_{18}, e_{18}, f_{19}Polygon(L_7, H_7, W_7, S_7) → q61, g_{19}, h_{19}, i_{19}, j_{19}Polygon(H_7, K_7, T_7, W_7) → q62, k_{19}, l_{19}, m_{19}, n_{19}Polygon(K_7, I_7, V_7, T_7) → q63, p_{19}, q_{19}, r_{19}, s_{19}Polygon(I_7, J_7, U_7, V_7) → q64, t_{19}, a_{19}, b_{19}, c_{19}
AI 绘图提示语参考
绘制一个由多个同心圆和连接圆心的线段组成的几何图形。首先绘制五个同心圆,每个圆的半径为0.125,然后连接每个圆的圆心,形成一个星形图案。接着绘制更多的同心圆和连接线段,形成复杂的几何结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。