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线性规划与多边形构造

线性规划与多边形构造
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2019-11-27 00:42
多边形解析几何最值优化几何作图
所属专题 Pyramid Puzzles
①本范例通过动态演示线性规划问题，直观展示最优解在多边形区域内的确定过程；②涉及核心数学概念包括线性不等式、可行域、最优解、多边形构造与坐标几何；③构造过程中运用了Polygon（多边形）、Midpoint（中点）等GeoGebra命令，以及A, B, C, D等对象来构建图形与轨迹；④适合高中及以上数学学习者，用于理解线性规划与解析几何的综合应用。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f_6, g_6, h, i, C, D
  2. Polygon(D, C, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a_6, b_6, I, J
  5. Polygon(J, I, 4) → poly5, c_6, d_5, e_5, f_1, K, L
  6. Midpoint(A, D) → M
  7. Midpoint(D, F) → N
  8. Midpoint(F, H) → O
  9. Midpoint(H, J) → P
  10. Midpoint(J, L) → Q
  11. Polygon(M, N, 4) → poly6, g_1, h_1, i_1, j_1, R, S
  12. Polygon(R, N, 4) → poly7, k_1, l_1, m_1, n_1, T, U
  13. Polygon(U, O, 4) → poly8, p_1, q_1, r_1, s_1, V, W
  14. Polygon(W, P, 4) → poly9, t_1, a_1, b_1, c_1, Z, A_1
  15. Midpoint(S, R) → B_1
  16. Midpoint(R, U) → C_1
  17. Midpoint(U, W) → D_1
  18. Midpoint(W, A_1) → E_1
  19. Polygon(B_1, C_1, 4) → poly10, d_1, e_1, f_2, g_2, F_1, G_1
  20. Polygon(F_1, C_1, 4) → poly11, h_2, i_2, j_2, k_2, H_1, I_1
  21. Polygon(I_1, D_1, 4) → poly12, l_2, m_2, n_2, p_2, J_1, K_1
  22. Midpoint(G_1, F_1) → L_1
  23. Midpoint(F_1, I_1) → M_1
  24. Midpoint(I_1, K_1) → N_1
  25. Polygon(L_1, M_1, 4) → poly13, q_2, r_2, s_2, t_2, O_1, P_1
  26. Polygon(O_1, M_1, 4) → poly14, a_2, b_2, c_2, d_2, Q_1, R_1
  27. Midpoint(P_1, O_1) → S_1
  28. Midpoint(O_1, R_1) → T_1
  29. Polygon(S_1, T_1, 4) → poly15, e_2, f_3, g_3, h_3, U_1, V_1
  30. Polygon(L, K, 4) → poly16, i_3, j_3, k_3, l_3, W_1, Z_1
  31. Polygon(Z_1, W_1, 4) → poly17, m_3, n_3, p_3, q_3, A_2, B_2
  32. Midpoint(L, Z_1) → C_2
  33. Midpoint(Z_1, B_2) → D_2
  34. Polygon(A_1, Q, 4) → poly18, r_3, s_3, t_3, a_3, E_2, F_2
  35. Polygon(F_2, C_2, 4) → poly19, b_3, c_3, d_3, e_3, G_2, H_2
  36. Midpoint(A_1, F_2) → I_2
  37. Midpoint(F_2, H_2) → J_2
  38. Polygon(K_1, E_1, 4) → poly20, f_4, g_4, h_4, i_4, K_2, L_2
  39. Polygon(L_2, I_2, 4) → poly21, j_4, k_4, l_4, m_4, M_2, N_2
  40. Midpoint(K_1, L_2) → O_2
  41. Midpoint(L_2, N_2) → P_2
  42. Polygon(R_1, N_1, 4) → poly22, n_4, p_4, q_4, r_4, Q_2, R_2
  43. Polygon(R_2, O_2, 4) → poly23, s_4, t_4, a_4, b_4, S_2, T_2
  44. Midpoint(R_1, R_2) → U_2
  45. Midpoint(R_2, T_2) → V_2
  46. Polygon(U_1, T_1, 4) → poly24, c_4, d_4, e_4, f_5, W_2, Z_2
  47. Polygon(Z_2, U_2, 4) → poly25, g_5, h_5, i_5, j_5, A_3, B_3
  48. Midpoint(V_1, U_1) → C_3
  49. Midpoint(U_1, Z_2) → D_3
  50. Polygon(C_3, D_3, 4) → poly26, k_5, l_5, m_5, n_5, E_3, F_3
  51. Polygon(E_3, D_3, 4) → poly27, p_5, q_5, r_5, s_5, G_3, H_3
  52. Midpoint(F_3, E_3) → I_3
  53. Midpoint(E_3, H_3) → J_3
  54. Polygon(I_3, J_3, 4) → poly28, t_5, a_5, b_5, c_5, K_3, L_3