动态演示尺规三等分线段的方法

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], B) → A'
3. Circle(A, A') → c
4. Dilate(B, If[1 < a ≤ 2, 2 - a, 0], A) → B'
5. Circle(B, B') → d
6. Intersect(c, d, 1) → C
7. Intersect(c, d, 2) → D
8. Rotate(B, If[2 < a ≤ 3, ((a - 2) * π / 3), π / 3], A) → B'_1
9. Rotate(B, If[2 < a ≤ 3, ((-(a - 2)) * π / 3), ((-π)) / 3], A) → B'_2
10. Dilate(B'_2, If[3 < a ≤ 4, 4 - a, 0], A) → E
11. Line(B, B'_2) → g
12. Line(A, B'_2) → i
13. Line(B'_2, A) → h
14. Line(B'_2, B) → j
15. Intersect(c_1, h) → F, G
16. Intersect(d_1, j) → H, I
17. Line(G, B) → k
18. Line(I, A) → l
19. Line(B'_1, A) → m
20. Line(B'_1, B) → n
21. Intersect(k, m) → J
22. Intersect(l, n) → K
23. Line(B'_2, K) → p
24. Line(B'_2, J) → q
25. Intersect(q, f) → L
26. Intersect(p, f) → M
27. Dilate(B'_2, If[3 < a ≤ 4, 4 - a, 0], G) → N
28. Dilate(B'_2, If[4 < a ≤ 5, 5 - a, 0], I) → O
29. Segment(B'_2, N) → r
30. Segment(B'_2, O) → s
31. Rotate(A, If[5.5 < a ≤ 6.5, ((a - 5.5) * π / 3), π / 3], A) → A'_1
32. Rotate(B, If[5.5 < a ≤ 6.5, ((a - 5.5) * π / 3), π / 3], A) → B'_3
33. Segment(A'_1, B'_3) → f'
34. Rotate(A, If[5.5 < a ≤ 7.5, ((-(a - 6.5)) * π / 3), ((-π)) / 3], B) → A'_2
35. Rotate(B, If[5.5 < a ≤ 7.5, ((-(a - 6.5)) * π / 3), ((-π)) / 3], B) → B'_4
36. Segment(A'_2, B'_4) → f'_1
37. Dilate(G, If[8 < a ≤ 9, 9 - a, 0], J) → G'
38. Dilate(J, If[9 < a ≤ 10, 10 - a, 0], B) → J'
39. Dilate(I, If[10 < a ≤ 11, 11 - a, 0], K) → I'
40. Dilate(K, If[11 < a ≤ 12, 12 - a, 0], A) → K'
41. Segment(G, G') → t
42. Segment(J, J') → b
43. Segment(I, I') → e
44. Segment(K, K') → f_1
45. Dilate(J, If[12.5 < a ≤ 13.5, 13.5 - a, 0], L) → J'_1
46. Dilate(K, If[12.5 < a ≤ 13.5, 13.5 - a, 0], M) → K'_1
47. Segment(J, J'_1) → g_1
48. Segment(K, K'_1) → h_1
49. Dilate(L, If[13.5 < a ≤ 14.5, 14.5 - a, 0], B'_2) → L'
50. Dilate(M, If[13.5 < a ≤ 14.5, 14.5 - a, 0], B'_2) → M'
51. Segment(L, L') → i_1
52. Segment(M, M') → j_1
53. Dilate(A, If[15.5 < a ≤ 16.5, 16.5 - a, 0], L) → A'_3
54. Segment(A, A'_3) → k_1
55. Dilate(L, If[16.5 < a ≤ 17.5, 17.5 - a, 0], M) → L'_1
56. Segment(L, L'_1) → l_1
57. Dilate(M, If[17.5 < a ≤ 18.5, 18.5 - a, 0], B) → M'_1
58. Segment(M, M'_1) → m_1
59. Rotate(A, If[18.5 < a ≤ 19.5, ((a - 18.5) * π), π], L) → A'_4
60. Rotate(A'_3, If[18.5 < a ≤ 19.5, ((a - 18.5) * π), π], L) → P
61. Segment(A'_4, P) → n_1
62. Rotate(A'_4, If[19.5 < a ≤ 20.5, ((a - 19.5) * π), π], M) → Q
63. Rotate(P, If[19.5 < a ≤ 20.5, ((a - 19.5) * π), π], M) → P'
64. Segment(Q, P') → p_1