GeoGebra 五格拼图
几何画板及绘图内容加载中,请稍等……
①本范例演示使用五格拼图进行几何拼接与挑战选择;②涉及核心数学概念包括几何变换、多边形拼接、空间想象;③作图要点:运用了 Circle, Point, Line, OrthogonalLine, Intersect, Vector, Translate, Segment, Polygon, Mirror 等GeoGebra命令与对象;④适合初中及以上学生用于几何学习与空间能力培养。
GeoGebra 命令及参数
Circle(D, a) → cCircle(D, (4 * a)) → kPoint(k) → MLine(D, M) → dOrthogonalLine(D, d) → eIntersect(c, e, 2) → EIntersect(c, e, 1) → FIntersect(c, d, 1) → GIntersect(c, d, 2) → HLine(E, d) → fLine(F, d) → gLine(H, e) → hLine(G, e) → iIntersect(f, i) → IIntersect(g, i) → JIntersect(f, h) → KIntersect(g, h) → LVector(J, L) → wVector(J, I) → zTranslate(K, w) → K'_1Translate(L, w) → L'Translate(K'_1, w) → K''_1Translate(L', w) → L''Translate(I, z) → I'_1Translate(K, z) → K'Vector(K, I) → jTranslate(I'_1, j) → I''_1Translate(I, j) → I'Point(d) → NCircle(N, flipcircle) → pIntersect(p, d, 1) → OIntersect(p, d, 2) → PSegment(O, P) → lPoint(l) → QSegment(O, Q) → mPolygon(I''_1, I', I, J, L'', K''_1, K, K') → poly1, i'', i', i_1, j_1, l'', k'', k_1, k'Mirror(I''_1, l) → I'''Mirror(I'_1, l) → SMirror(K', l) → K''Mirror(I', l) → I''Polygon(I''', K'', L, L'', K''_1, I, J, I'') → poly2, i''', k''_1, l_1, l''_1, k''_2, i_2, j_2, i''_1Circle(T, a) → rCircle(T, (6 * a)) → sPoint(s) → ULine(T, U) → tOrthogonalLine(T, t) → a_1Intersect(r, a_1, 2) → VIntersect(r, t, 1) → WIntersect(r, a_1, 1) → ZIntersect(r, t, 2) → A_1Line(V, t) → b_1Line(Z, t) → c_1Line(W, a_1) → d_1Line(A_1, a_1) → e_1Intersect(b_1, d_1) → B_1Intersect(c_1, d_1) → C_1Intersect(c_1, e_1) → D_1Intersect(b_1, e_1) → E_1Vector(C_1, D_1) → uVector(C_1, B_1) → vVector(E_1, D_1) → nVector(E_1, B_1) → qTranslate(D_1, Vector[(3 * u)]) → ATranslate(E_1, Vector[(3 * u)]) → BTranslate(B_1, v) → CTranslate(E_1, v) → RMirror(C, t) → C'Mirror(R, t) → R'Point(t) → F_1Point(t) → G_1Segment(F_1, G_1) → f_1Point(f_1) → H_1Segment(F_1, H_1) → g_1Polygon(C, C_1, A, B, E_1, R) → poly3, c_2, c_3, a_2, b_2, e_2, r_1Polygon(C', R', D_1, A, B, B_1) → poly4, c', r', d_2, a_3, b_3, b_4Circle(I_1, a) → h_1Circle(I_1, (4 * a)) → p_1Point(p_1) → J_1Line(I_1, J_1) → m_1OrthogonalLine(I_1, m_1) → n_1Intersect(h_1, n_1, 2) → K_1Intersect(h_1, m_1, 1) → L_1Intersect(h_1, n_1, 1) → M_1Intersect(h_1, m_1, 2) → N_1Line(K_1, m_1) → q_1Line(M_1, m_1) → s_1Line(L_1, n_1) → t_1Line(N_1, n_1) → f_2Intersect(q_1, t_1) → O_1Intersect(s_1, t_1) → P_1Intersect(s_1, f_2) → Q_1Intersect(q_1, f_2) → R_1Vector(P_1, Q_1) → u_1Vector(P_1, O_1) → v_1Translate(Q_1, Vector[(2 * u_1)]) → T_1Translate(R_1, u_1) → S_1Translate(T_1, Vector[(2 * v_1)]) → U_1Translate(S_1, v_1) → V_1Translate(P_1, Vector[(-1 * v_1)]) → W_1Translate(Q_1, Vector[(-1 * v_1)]) → Z_1Polygon(Z_1, Q_1, T_1, U_1, V_1, S_1, O_1, W_1) → poly5, z_1, q_2, t_2, u_2, v_2, s_2, o_1, w_1Mirror(W_1, m_1) → D_2Mirror(Z_1, m_1) → E_2Mirror(V_1, m_1) → F_2Mirror(U_1, m_1) → G_2Translate(T_1, v_1) → I_2Point(m_1) → A_2Point(m_1) → B_2Point(m_1) → C_2Segment(A_2, C_2) → g_2Point(g_2) → H_2Segment(H_2, A_2) → h_2Translate(F_2, v_1) → J_2Polygon(D_2, P_1, J_2, F_2, G_2, I_2, R_1, E_2) → poly6, d_3, p_2, j_3, f_3, g_3, i_3, r_2, e_3Circle(K_2, a) → k_2Circle(K_2, (4 * a)) → h_3Point(h_3) → L_2Line(K_2, L_2) → l_2OrthogonalLine(K_2, l_2) → m_2Intersect(k_2, m_2, 2) → M_2Intersect(k_2, l_2, 1) → N_2Intersect(k_2, m_2, 1) → O_2Intersect(k_2, l_2, 2) → P_2Line(M_2, l_2) → n_2Line(O_2, l_2) → k_3Line(N_2, m_2) → l_3Line(P_2, m_2) → m_3Intersect(n_2, l_3) → Q_2Intersect(k_3, l_3) → R_2Intersect(k_3, m_3) → S_2Intersect(n_2, m_3) → T_2Vector(R_2, S_2) → w_2Vector(R_2, Q_2) → z_2Translate(S_2, w_2) → U_2Translate(U_2, w_2) → V_2Translate(T_2, w_2) → W_2Translate(W_2, w_2) → Z_2Translate(T_2, z_2) → A_3Translate(W_2, z_2) → B_3Translate(U_2, Vector[(-1 * z_2)]) → C_3Translate(V_2, Vector[(-1 * z_2)]) → D_3Point(l_2) → E_3Point(l_2) → F_3Segment(E_3, F_3) → n_3Point(n_3) → G_3Segment(E_3, G_3) → p_3Polygon(R_2, U_2, C_3, D_3, Z_2, W_2, B_3, A_3, T_2, Q_2) → poly7, r_3, q_3, u_3, c_4, d_4, z_3, w_3, b_5, a_4, t_3Mirror(A_3, l_2) → H_3Mirror(D_3, l_2) → I_3Polygon(R_2, S_2, H_3, C_3, U_2, V_2, I_3, B_3, W_2, Q_2) → poly8, r_4, q_4, s_3, h_4, c_5, u_4, v_3, i_4, b_6, w_4Circle(J_3, a) → e_4Circle(J_3, (6 * a)) → f_4Point(f_4) → K_3Line(J_3, K_3) → g_4OrthogonalLine(J_3, g_4) → j_4Intersect(e_4, j_4, 2) → L_3Intersect(e_4, g_4, 1) → M_3Intersect(e_4, j_4, 1) → N_3Intersect(e_4, g_4, 2) → O_3Line(L_3, g_4) → k_4Line(N_3, g_4) → l_4Line(M_3, j_4) → m_4Line(O_3, j_4) → n_4Intersect(k_4, m_4) → P_3Intersect(l_4, m_4) → Q_3Intersect(l_4, n_4) → R_3Intersect(k_4, n_4) → S_3Vector(Q_3, R_3) → v_4Vector(Q_3, P_3) → z_4Translate(R_3, v_4) → T_3Translate(T_3, v_4) → U_3Translate(U_3, v_4) → V_3Translate(S_3, v_4) → W_3Translate(W_3, v_4) → Z_3Translate(Z_3, v_4) → A_4Translate(S_3, z_4) → B_4Translate(W_3, z_4) → C_4Mirror(B_4, g_4) → D_4Mirror(C_4, g_4) → E_4Point(g_4) → G_4Point(g_4) → H_4Segment(G_4, H_4) → p_4Point(p_4) → I_4Segment(G_4, I_4) → s_4Polygon(Q_3, V_3, A_4, W_3, C_4, B_4, S_3, P_3) → poly9, q_5, v_5, a_5, w_5, c_6, b_7, s_5, p_5Polygon(P_3, A_4, V_3, T_3, E_4, D_4, R_3, Q_3) → poly10, p_6, a_6, v_6, t_4, e_5, d_5, r_5, q_6Circle(J_4, a) → f_5Circle(J_4, (4 * a)) → g_5Point(g_5) → K_4Line(J_4, K_4) → h_5OrthogonalLine(J_4, h_5) → i_5Intersect(f_5, i_5, 2) → L_4Intersect(f_5, i_5, 1) → M_4Intersect(f_5, h_5, 1) → N_4Intersect(f_5, h_5, 2) → O_4Line(L_4, h_5) → j_5Line(M_4, h_5) → k_5Line(N_4, i_5) → l_5Line(O_4, i_5) → m_5Intersect(j_5, l_5) → P_4Intersect(k_5, l_5) → Q_4Intersect(k_5, m_5) → R_4Intersect(j_5, m_5) → S_4Vector(Q_4, P_4) → u_5Vector(Q_4, R_4) → z_5Translate(R_4, z_5) → T_4Translate(T_4, z_5) → U_4Translate(P_4, u_5) → V_4Translate(V_4, z_5) → W_4Translate(W_4, z_5) → Z_4Translate(T_4, u_5) → A_5Translate(U_4, u_5) → B_5Point(h_5) → C_5Point(h_5) → D_5Mirror(V_4, h_5) → E_5Mirror(W_4, h_5) → F_5Mirror(Z_4, h_5) → G_5Segment(C_5, D_5) → n_5Point(n_5) → H_5Segment(C_5, H_5) → t_5Polygon(V_4, Q_4, U_4, B_5, A_5, Z_4) → poly11, v_7, q_7, u_6, b_8, a_7, z_6Polygon(P_4, B_5, U_4, T_4, G_5, E_5) → poly12, p_7, b_9, u_7, t_6, g_6, e_6Circle(I_5, a) → d_6Circle(I_5, (8 * a)) → f_6Point(f_6) → J_5Line(I_5, J_5) → h_6OrthogonalLine(I_5, h_6) → i_6Intersect(d_6, i_6, 2) → K_5Intersect(d_6, h_6, 1) → L_5Intersect(d_6, i_6, 1) → M_5Intersect(d_6, h_6, 2) → N_5Line(K_5, h_6) → j_6Line(M_5, h_6) → k_6Line(L_5, i_6) → l_6Line(N_5, i_6) → m_6Intersect(j_6, l_6) → O_5Intersect(k_6, l_6) → P_5Intersect(k_6, m_6) → Q_5Intersect(j_6, m_6) → R_5Vector(P_5, Q_5) → w_6Translate(Q_5, Vector[(4 * w_6)]) → S_5Translate(R_5, Vector[(4 * w_6)]) → T_5Polygon(P_5, S_5, T_5, O_5) → poly13, p_8, s_6, t_7, o_5Circle(U_5, a) → r_6Circle(U_5, (4 * a)) → c_7Point(c_7) → V_5Line(U_5, V_5) → n_6OrthogonalLine(U_5, n_6) → d_7Intersect(r_6, d_7, 2) → W_5Intersect(r_6, d_7, 1) → Z_5Intersect(r_6, n_6, 1) → A_6Intersect(r_6, n_6, 2) → B_6Line(W_5, n_6) → e_7Line(Z_5, n_6) → f_7Line(A_6, d_7) → g_7Line(B_6, d_7) → h_7Intersect(e_7, g_7) → C_6Intersect(f_7, g_7) → D_6Intersect(f_7, h_7) → E_6Intersect(e_7, h_7) → F_6Vector(D_6, E_6) → w_7Vector(D_6, C_6) → z_7Vector(F_6, E_6) → i_7Translate(E_6, i_7) → G_6Translate(G_6, w_7) → H_6Translate(H_6, z_7) → I_6Translate(I_6, w_7) → J_6Translate(J_6, z_7) → K_6Translate(F_6, w_7) → L_6Translate(L_6, z_7) → M_6Translate(F_6, z_7) → N_6Polygon(D_6, E_6, F_6, C_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6) → poly14, d_8, n_7, f_8, c_8, e_8, g_8, h_8, i_8, j_7, k_7, l_7, m_7Circle(O_6, a) → r_7Circle(O_6, (4 * a)) → s_7Point(s_7) → P_6Line(O_6, P_6) → a_8OrthogonalLine(O_6, a_8) → j_8Intersect(r_7, j_8, 2) → Q_6Intersect(r_7, a_8, 1) → R_6Intersect(r_7, j_8, 1) → S_6Intersect(r_7, a_8, 2) → T_6Line(Q_6, a_8) → k_8Line(S_6, a_8) → l_8Line(R_6, j_8) → m_8Line(T_6, j_8) → n_8Intersect(k_8, m_8) → U_6Intersect(l_8, m_8) → V_6Intersect(l_8, n_8) → W_6Intersect(k_8, n_8) → Z_6Vector(V_6, W_6) → u_8Vector(V_6, U_6) → v_8Translate(W_6, Vector[(2 * u_8)]) → A_7Translate(Z_6, Vector[(2 * u_8)]) → B_7Translate(U_6, Vector[(2 * v_8)]) → C_7Translate(Z_6, Vector[(2 * v_8)]) → D_7Polygon(V_6, A_7, B_7, Z_6, D_7, C_7) → poly15, v_9, a_9, b_{10}, z_8, d_9, c_9Circle(E_7, a) → q_8Circle(E_7, (4 * a)) → r_8Point(r_8) → F_7Line(E_7, F_7) → s_8OrthogonalLine(E_7, s_8) → t_8Intersect(q_8, t_8, 2) → G_7Intersect(q_8, s_8, 1) → H_7Intersect(q_8, t_8, 1) → I_7Intersect(q_8, s_8, 2) → J_7Line(G_7, s_8) → e_9Line(I_7, s_8) → f_9Line(H_7, t_8) → g_9Line(J_7, t_8) → h_9Intersect(e_9, g_9) → K_7Intersect(f_9, g_9) → L_7Intersect(f_9, h_9) → M_7Intersect(e_9, h_9) → N_7Vector(L_7, M_7) → w_8Vector(L_7, K_7) → u_9Translate(M_7, Vector[(2 * w_8)]) → O_7Translate(N_7, Vector[(2 * w_8)]) → P_7Translate(N_7, w_8) → Q_7Translate(N_7, Vector[(2 * u_9)]) → R_7Translate(Q_7, Vector[(2 * u_9)]) → S_7Polygon(L_7, O_7, P_7, Q_7, S_7, R_7, N_7, K_7) → poly16, l_9, o_7, p_9, q_9, s_9, r_9, n_9, k_9Circle(T_7, a) → t_9Circle(T_7, (2 * a)) → c_{10}Point(c_{10}) → U_7Line(T_7, U_7) → i_9OrthogonalLine(T_7, i_9) → j_9Intersect(t_9, j_9, 2) → V_7Intersect(t_9, i_9, 1) → W_7Intersect(t_9, j_9, 1) → Z_7Intersect(t_9, i_9, 2) → A_8Line(V_7, i_9) → m_9Line(Z_7, i_9) → a_{10}Line(W_7, j_9) → d_{10}Line(A_8, j_9) → e_{10}Intersect(m_9, d_{10}) → B_8Intersect(a_{10}, d_{10}) → C_8Intersect(a_{10}, e_{10}) → D_8Intersect(m_9, e_{10}) → E_8Vector(C_8, D_8) → w_9Vector(C_8, B_8) → z_9Vector(E_8, D_8) → u_{10}Vector(E_8, B_8) → v_{10}Translate(D_8, w_9) → F_8Translate(F_8, z_9) → G_8Translate(G_8, z_9) → H_8Translate(E_8, z_9) → I_8Translate(B_8, z_9) → J_8Translate(J_8, v_{10}) → K_8Translate(C_8, v_{10}) → L_8Polygon(L_8, F_8, H_8, I_8, E_8, B_8, J_8, K_8) → poly17, l_{10}, f_{10}, h_{10}, i_{10}, e_{11}, b_{11}, j_{10}, k_{10}Circle(M_8, a) → g_{10}Circle(M_8, (2 * a)) → p_{10}Point(p_{10}) → N_8Line(M_8, N_8) → m_{10}OrthogonalLine(M_8, m_{10}) → n_{10}Intersect(g_{10}, n_{10}, 2) → O_8Intersect(g_{10}, m_{10}, 1) → P_8Intersect(g_{10}, n_{10}, 1) → Q_8Intersect(g_{10}, m_{10}, 2) → R_8Line(O_8, m_{10}) → q_{10}Line(Q_8, m_{10}) → r_{10}Line(P_8, n_{10}) → s_{10}Line(R_8, n_{10}) → t_{10}Intersect(q_{10}, s_{10}) → S_8Intersect(r_{10}, s_{10}) → T_8Intersect(r_{10}, t_{10}) → U_8Intersect(q_{10}, t_{10}) → V_8Vector(T_8, U_8) → w_{10}Vector(V_8, S_8) → z_{10}Vector(T_8, S_8) → u_{11}Vector(V_8, U_8) → v_{11}Translate(U_8, w_{10}) → W_8Translate(V_8, w_{10}) → Z_8Translate(V_8, u_{11}) → A_9Translate(S_8, u_{11}) → B_9Translate(S_8, z_{10}) → C_9Translate(C_9, u_{11}) → D_9Translate(D_9, u_{11}) → E_9Translate(B_9, u_{11}) → F_9Polygon(T_8, W_8, Z_8, V_8, A_9, B_9, F_9, E_9, C_9, S_8) → poly18, t_{11}, s_{11}, w_{11}, z_{11}, v_{12}, a_{11}, b_{12}, f_{11}, e_{12}, c_{11}Polygon(G_9, H_9, J_9, I_9) → poly19, g_{11}, h_{11}, j_{11}, i_{11}Polygon(G_9, L_9, K_9, M_9) → poly20, g_{12}, l_{11}, k_{11}, m_{11}
AI 绘图提示语参考
绘制一个由多个五边形组成的几何图形。首先画一个圆 c,然后画一个更大的圆 k,从中选取点 M。通过 M 画一条线 d,再画 d 的垂线 e,与圆 c 交于 E 和 F。接着画 d 和 e 的交点 G 和 H,以及 f、g、h、i 等线段和点,通过平移和镜像操作,最终形成两个五边形 poly1 和 poly2。
以上提示语为根据原始绘图命令整理而来,仅供参考。