MMC示例2
几何画板及绘图内容加载中,请稍等……
该范例演示了MMC(最大最小值)问题的几何构造。核心数学概念包括几何作图、优化与线性规划。通过使用GeoGebra命令如Point、Polygon、Midpoint等,用户可以直观地理解如何通过几何构造找到最优解。适合高中数学教学和学习。
GeoGebra 命令及参数
Point(xAxis) → UPoint(xAxis) → VPolygon(U, V, 4) → pol6, n, p, b, h_1, W, ZMidpoint(n) → A_1OrthogonalLine(A_1, n) → i_1Midpoint(p) → B_1OrthogonalLine(B_1, i_1) → m_1Intersect(i_1, m_1) → C_1Circle(C_1, (sqrt(31) - 1) / 5) → c_1Intersect(c_1, m_1, 2) → D_1Intersect(c_1, i_1) → E_1, F_1Mirror(D_1, i_1) → G_1Line(D_1, i_1) → n_1Line(E_1, m_1) → p_1Intersect(n_1, p_1) → H_1Mirror(H_1, i_1) → I_1Mirror(I_1, m_1) → J_1Mirror(J_1, i_1) → K_1Midpoint(K_1, F_1) → L_1Line(K_1, J_1) → d_1Circle(L_1, 0.15) → e_1Intersect(e_1, d_1) → M_1, N_1OrthogonalLine(L_1, d_1) → f_2Circle(L_1, (4 - (4 * (sqrt(31) - 1) / 5)) / 3) → c_2Intersect(f_2, pol6) → O_1, P_1Intersect(c_2, f_2) → Q_1, R_1OrthogonalLine(Q_1, f_2) → i_2OrthogonalLine(M_1, d_1) → k_2OrthogonalLine(N_1, d_1) → n_2Intersect(i_2, k_2) → S_1Intersect(i_2, n_2) → V_1Intersect(h_1, m_1) → W_1Intersect(i_1, b) → Z_1Polygon(Z, W_1, D_1, K_1, M_1, S_1, V_1, N_1, F_1, Z_1) → pol4, z_1, i_3, w_1, t_2, a_2, b_2, d_2, v_1, e_2, h_3Mirror(Z, i_1) → Z'Mirror(W_1, i_1) → AMirror(D_1, i_1) → BMirror(K_1, i_1) → CMirror(M_1, i_1) → DMirror(S_1, i_1) → EMirror(V_1, i_1) → FMirror(N_1, i_1) → GMirror(F_1, i_1) → HMirror(Z_1, i_1) → IPolygon(Z', A, B, C, D, E, F, G, H, I) → pol5, z', i, a, b_1, c, d, e, f, g, hMirror(Z, m_1) → Z'_{1}Mirror(W_1, m_1) → JMirror(D_1, m_1) → KMirror(K_1, m_1) → LMirror(M_1, m_1) → MMirror(S_1, m_1) → NMirror(V_1, m_1) → OMirror(N_1, m_1) → PMirror(F_1, m_1) → QMirror(Z_1, m_1) → RPolygon(Z'_{1}, J, K, L, M, N, O, P, Q, R) → pol3, z'_{1}, r, j, k, l, m, n_3, o, p_2, qMirror(Z', m_1) → Z''Mirror(A, m_1) → A'Mirror(B, m_1) → B'Mirror(C, m_1) → C'Mirror(D, m_1) → D'Mirror(E, m_1) → E'Mirror(F, m_1) → F'Mirror(G, m_1) → G'Mirror(H, m_1) → H'Mirror(I, m_1) → I'Polygon(Z'', A', B', C', D', E', F', G', H', I') → pol2, z'', i', a', b', c', d', e', f', g', h'Polygon(K_1, H_1, I_1, J_1, D, E, F, G, N_1, V_1, S_1, M_1, M, N, O, P, G', F', E', D') → pol1, k_1, j_1, l_1, q_1, d_3, e_3, f_3, g_2, r_1, s_1, t_1, s, a_1, m_2, n_4, o_1, p_3, t, f_1, g_1Perimeter(pol2) → Perímetro_{pol2}Perimeter(pol1) → Perímetro_{pol1}Prism(pol3, n) → h_2, S, F_2, face1, face2, face3, face4, face5, face6, face7, face8, face9, T, face10, face11, aresta1, aresta2, aresta3, aresta4, aresta5, aresta6, aresta7, aresta8, T_1, aresta9, aresta10, aresta11, aresta12, aresta13, aresta14, aresta15, aresta16, aresta17, aresta18, U_1, aresta19, aresta20, A_2, B_2, C_2, D_2, E_2
AI 绘图提示语参考
在坐标轴上取两个点,以它们为顶点构造一个正方形。找到正方形一条边的中点,过该中点作此边的垂线;再取相邻边的中点,作该垂线的垂线,两线交于一点。以该点为圆心,以特定半径作圆,圆与垂线相交得到若干点。通过对称和连线,构造一个由多个点围成的多边形,并对其关于某条线作镜像,得到对称的另一多边形。整体呈现对称的几何构图,包含圆、垂线、多边形及镜像关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。