哪个线段更长？几何与三角函数的视觉错觉

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Rotate(A, pi / 4, B) → A'
3. Mirror(A', f) → A''
4. Ray(B, A') → g
5. Ray(B, A'') → h
6. Circle(B, (0.3 * f)) → c
7. Intersect(c, h, 1) → C
8. Intersect(c, g, 1) → D
9. Segment(B, D) → i
10. Segment(B, C) → j
11. Midpoint(f) → E
12. Mirror(c, E) → c'
13. OrthogonalLine(E, f) → k
14. Mirror(C, k) → C'
15. Mirror(D, k) → D'
16. Segment(A, C') → l
17. Segment(A, D') → m
18. Line(F, f) → n
19. Circle(F, Distance[A, B]) → d
20. Intersect(d, n, 2) → G
21. Segment(F, G) → p
22. Rotate(F, (-3 * pi / 4), G) → F'
23. Mirror(F', p) → F''
24. LineBisector(p) → q
25. Mirror(F', q) → F''_{1}
26. Mirror(F'', q) → F'''
27. Ray(G, F') → r
28. Ray(G, F'') → s
29. Ray(F, F''_{1}) → t
30. Ray(F, F''') → a
31. Circle(G, Distance[B, C]) → e
32. Circle(F, Distance[B, C]) → c_1
33. Intersect(c_1, t, 1) → H
34. Intersect(c_1, a, 1) → I
35. Intersect(e, r) → J,
36. Intersect(e, s, 1) → K
37. Segment(G, J) → b
38. Segment(G, K) → f_1
39. Segment(F, H) → g_1
40. Segment(F, I) → h_1
41. Dilate(F, If[0 < o ≤ 1, 1 - o, 0], A) → F'_{1}
42. Vector(F, F'_{1}) → u
43. Translate(F, u) → F'_{2}
44. Translate(G, u) → G'
45. Segment(F'_{2}, G') → p'