梯子下落问题：动态调整与微积分应用

GeoGebra 命令及参数

1. Circle(B, 10) → c
2. Intersect(c, f, 1) → C
3. Segment(B, C) → g
4. Ray(A, D) → h
5. Ray(A, E) → i
6. Circle(B, 1) → d
7. Intersect(d, i, 2) → F
8. Circle(D, 1) → e
9. Intersect(f, h) → G
10. Intersect(f, h) → H
11. Intersect(f, h) → I
12. Intersect(e, f) → J, K
13. Ray(C, J) → j
14. Ray(B, F) → k
15. Segment(A, B) → l
16. Segment(A, C) → m
17. Angle(E, A, D) → α
18. Polygon(A, B, C) → poly1, c_1, a_1, b
19. Circle(C, 1) → p
20. Intersect(p, g, 1) → L
21. Circle(L, 1) → q
22. Intersect(q, g, 1) → M
23. Circle(M, 1) → r
24. Intersect(r, g, 1) → N
25. Circle(N, 1) → s
26. Intersect(s, g, 1) → O
27. Circle(O, 1) → t
28. Intersect(t, g, 1) → P
29. Circle(P, 1) → d_1
30. Intersect(d_1, g, 1) → Q
31. Circle(Q, 1) → e_1
32. Intersect(e_1, g, 1) → R
33. Circle(R, 1) → f_1
34. Intersect(f_1, g, 1) → S
35. Circle(S, 1) → g_1
36. Intersect(g_1, g, 1) → T
37. OrthogonalLine(L, g) → n
38. OrthogonalLine(M, g) → h_1
39. OrthogonalLine(N, g) → i_1
40. OrthogonalLine(O, g) → j_1
41. OrthogonalLine(P, g) → k_1
42. OrthogonalLine(Q, g) → l_1
43. OrthogonalLine(R, g) → m_1
44. OrthogonalLine(S, g) → n_1
45. OrthogonalLine(T, g) → p_1
46. Intersect(q, n, 1) → U
47. Intersect(r, h_1, 1) → V
48. Intersect(s, i_1, 1) → W
49. Intersect(t, j_1, 1) → Z
50. Intersect(d_1, k_1, 1) → A_1
51. Intersect(e_1, l_1, 1) → B_1
52. Intersect(f_1, m_1, 1) → C_1
53. Intersect(g_1, n_1, 1) → D_1
54. Circle(T, 1) → q_1
55. Intersect(q_1, p_1, 1) → E_1
56. Vector(M, V) → u
57. Translate(B, u) → B'
58. Translate(C, u) → C'
59. Segment(B', C') → g'
60. Segment(L, U) → r_1
61. Segment(M, V) → s_1
62. Segment(N, W) → t_1
63. Segment(O, Z) → b_1
64. Segment(P, A_1) → f_2
65. Segment(Q, B_1) → g_2
66. Segment(R, C_1) → h_2
67. Segment(S, D_1) → i_2
68. Segment(T, E_1) → j_2
69. Distance(B, C) → distanceBC
70. Textfield(a) → InputBox1
71. Textfield(o) → InputBox2
72. Distance(A, B) → distanceAB
73. Distance(A, C) → distanceAC
74. Distance(A, B) → v
75. Distance(A, C) → w