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卡纸盒体积最大化

卡纸盒体积最大化
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2015-02-26 01:49
立体几何微积分最值优化几何作图
①本范例演示如何通过从卡纸角剪去正方形来最大化盒子的体积；②涉及核心数学概念包括体积计算、优化问题、相似三角形和导数应用；③作图要点使用了PointList, Point, Polygon, Intersect等GeoGebra命令与对象来构建和计算；④适合高中数学教学，用于理解实际应用中的微积分和几何优化问题。

GeoGebra 命令及参数

  1. PointList(Transpose[(PM * Transpose[FL])]) → FP
  2. PointList(Transpose[(PM * Transpose[ML])]) → MP
  3. Point(FP) → A
  4. Point(FP) → B
  5. Point(FP) → C
  6. Point(FP) → D
  7. Polygon(A, B, C, D) → poly1, a, b, c, d
  8. Intersect(b, a) → E
  9. Point(MP) → F
  10. Point(MP) → G
  11. Intersect(c, b) → H
  12. Polygon(E, F, G, H) → poly2, e, f, g, h_1
  13. Intersect(c, b) → I
  14. Intersect(d, c) → J
  15. Point(MP) → K
  16. Point(MP) → L
  17. Polygon(I, J, K, L) → poly3, i, j, k, l_1
  18. Intersect(d, a) → M
  19. Intersect(d, c) → N
  20. Point(MP) → O
  21. Point(MP) → P
  22. Polygon(N, M, O, P) → poly4, n, m, o, p
  23. Intersect(b, a) → Q
  24. Point(MP) → R
  25. Point(MP) → S
  26. Intersect(d, a) → T
  27. Polygon(Q, R, S, T) → poly5, q_1, r, s, t
  28. Intersect(r, q_1) → U
  29. Point(FP) → V
  30. Intersect(f, e) → W
  31. Intersect(b, a) → Z
  32. Polygon(U, V, W, Z) → poly6, u, v, w_1, z
  33. Intersect(g, f) → A_1
  34. Intersect(c, b) → B_1
  35. Intersect(l_1, k) → C_1
  36. Point(FP) → D_1
  37. Polygon(A_1, B_1, C_1, D_1) → poly7, a_1, b_1, c_1, d_1
  38. Intersect(s, r) → E_1
  39. Point(FP) → F_1
  40. Intersect(o, m) → G_1
  41. Intersect(d, a) → H_1
  42. Polygon(E_1, F_1, G_1, H_1) → poly8, e_1, f_1, g_1, h_2
  43. Intersect(j, p) → I_1
  44. Intersect(p, o) → J_1
  45. Point(FP) → K_1
  46. Intersect(k, j) → L_1
  47. Polygon(I_1, J_1, K_1, L_1) → poly9, i_1, j_1, k_1, l_2