折纸盒最大体积问题——动态模拟与极值求解

GeoGebra 命令及参数

1. Function(x * (length - 2 * x) * (width - 2 * x), 0, Vright) → V
2. Segment(B, C) → b
3. Rotate(B, α, A) → B'
4. Line(B', A) → s
5. Line(Ax, s) → s1
6. Segment(A, B) → a
7. Line(C, a) → r
8. Intersect(s, r) → D
9. Line(Dy, r) → r1
10. Intersect(r1, b) → Cy
11. Segment(Dy, Cy) → c1
12. Segment(C, D) → c
13. Intersect(s1, c) → Dx
14. Segment(Ax, Dx) → d1
15. Intersect(d1, c1) → D1
16. Line(B, s) → q
17. Line(Bx, q) → q1
18. Intersect(q1, c) → Cx
19. Segment(Bx, Cx) → b1
20. Intersect(b1, c1) → C1
21. Line(A, B) → p
22. Line(Ay, p) → p1
23. Intersect(p1, b) → By
24. Segment(Ay, By) → a1
25. Intersect(d1, a1) → A1
26. Intersect(b1, a1) → B1
27. Angle(B, A, B') → β
28. Segment(D, A) → d
29. Polygon(A1, A2a, B2a, B1) → poly1, e, f, g, h_1
30. Polygon(B1, B2b, C2b, C1) → poly2, i, j, k, l
31. Polygon(C1, C2c, D2c, D1) → poly3, c_1, d_1, e_1, f_1
32. Polygon(D1, D2d, A2d, A1) → poly4, m, n, a_1, b_1
33. Derivative(V) → Vder
34. Root(Vder) → tMax_1, tMax_2
35. Min(x(tMax_1), x(tMax_2)) → tMax
36. Segment(tMax_1, P) → g_1