无盖长方体优化问题
几何画板及绘图内容加载中,请稍等……
这是一个经典的优化问题可视化工具,演示如何通过调整长方体的尺寸来最大化其体积。核心数学概念包括几何作图、函数图像和最值优化。通过使用Polygon、Segment、Point等GeoGebra命令,用户可以直观地理解优化问题的构造过程。适合高中数学教学和学习。
GeoGebra 命令及参数
Polygon(A, B, D, C) → q1, a, b, d, c_1Polygon(A, E, 4) → poly1, f, g, h, i, F, GPolygon(H, C, 4) → poly2, j, k, l, m, I, JPolygon(K, L, N, M) → q2, k_1, l_1, n, m_1Polygon(L, B, O, N) → q3, l_2, b_1, o, n_1Polygon(Q, P, 4) → poly3, p, q, r, s, R, SPolygon(R, T, D, S) → q4, r_1, t, d_1, s_1Segment(J, F) → eSegment(F, M) → f_1Segment(M, P) → g_1Segment(P, J) → h_1Segment(R, N) → i_1Polygon(Q, P, T, D) → q5, q_1, p_1, t_1, d_2Polygon(M, K, B, O) → q6, m_2, k_2, b_2, o_1Point(Circle[W, 8 - (2 * c)]) → A_1Segment(W, A_1) → j_1Rotate(A_1, 35°, W) → B_1Segment(W, U) → a_1Segment(U, V) → e_1Segment(V, Z) → f_2Segment(Z, W) → g_2Segment(W, B_1) → h_2Line(Z, h_2) → i_2Line(B_1, g_2) → j_2Line(V, h_2) → n_2Intersect(i_2, j_2) → C_1Line(C_1, f_2) → p_2Intersect(n_2, p_2) → D_1Segment(W, B_1) → q_2Segment(B_1, C_1) → r_2Segment(C_1, Z) → s_2Segment(V, D_1) → t_2Segment(D_1, C_1) → a_2