三正方形问题：单位圆内接正方形的角度与相似变换探究

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Polygon(B, E, 4) → poly2, j, k, l, m, G, H
3. Polygon(E, F, 4) → poly3, n, p, q, r, I, J
4. Segment(A, B) → s
5. Segment(B, C) → t
6. Segment(C, D) → b
7. Segment(D, A) → c
8. Segment(C, G) → d
9. Segment(G, E) → e
10. Segment(E, B) → f_1
11. Segment(G, I) → g_1
12. Segment(I, F) → h_1
13. Segment(F, E) → i_1
14. Angle(C, B, A) → α
15. Angle(D, C, B) → β
16. Angle(A, D, C) → γ
17. Angle(C, G, E) → δ
18. Angle(G, E, B) → ε
19. Angle(I, F, E) → ζ
20. Circle(A, (0.25 * b)) → c_1
21. Circle(B, (0.25 * b)) → d_1
22. Circle(E, (0.25 * b)) → e_1
23. Segment(E, I) → j_1
24. Segment(B, I) → k_1
25. Segment(A, I) → l_1
26. Intersect(c_1, l_1, 1) → K
27. Intersect(c_1, s, 1) → L
28. Intersect(d_1, k_1, 1) → M
29. Intersect(d_1, f_1, 1) → N
30. Intersect(e_1, j_1, 1) → O
31. Intersect(e_1, i_1, 1) → P
32. Intersect(e_1, e, 1) → Q
33. CircleSector(B, N, M) → p_1
34. CircleSector(A, L, K) → q_1
35. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], I) → A'
36. Segment(A, A') → m_1
37. Dilate(I, If[1 < o ≤ 2, 2 - o, 0], B) → I'
38. Segment(I, I') → n_1
39. Dilate(E, If[2 < o ≤ 3, 3 - o, 0], I) → E'
40. Segment(E, E') → s_1
41. CircleSector(E, O, Q) → r_1
42. Rotate(r_1, If[4 < o ≤ 5, ((-(o - 4)) * π / 4), ((-π)) / 4], E) → t_1
43. Line(B, s_1) → a_1
44. Intersect(a_1, m_1) → S
45. Angle(N, B, S) → η
46. Rotate(p_1, If[5 < o ≤ 6, ((o - 5) * η), η], B) → c_2
47. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], E) → B'
48. Vector(B, B') → u
49. Translate(c_2, u) → d_2
50. CircleArc(B, N, M) → e_2
51. Line(A, s_1) → b_1
52. Angle(M, B, S) → θ
53. Angle(L, A, K) → ι
54. Rotate(q_1, If[7 < o ≤ 8, ((o - 7) * (π / 2 - θ)), π / 2 - θ], A) → f_2
55. Dilate(A, If[8 < o ≤ 9, 9 - o, 0], E) → A'_1
56. Vector(A, A'_1) → v
57. Translate(f_2, v) → g_2
58. CircleArc(A, L, K) → h_2