圆周率π的探索

GeoGebra 命令及参数

1. Circle(A, 1) → c
2. Point(c) → B
3. Rotate(B, (-a), A) → B'
4. CircleArc(A, B, B') → d
5. Intersect(xAxis, yAxis) → D
6. Segment(D, B) → b
7. Point(yAxis) → C
8. Point(b) → E
9. Circle(C, E) → e
10. Point(c) → F
11. Line(F, A) → f
12. Point(f) → G
13. Circle(A, 0.5) → g
14. Segment(G, A) → h
15. Rotate(f, (-a), A) → f'
16. Intersect(g, f', 1) → H
17. Intersect(g, f', 2) → I
18. Segment(H, A) → i
19. Segment(I, A) → j
20. Line(H, xAxis) → k
21. Line(I, xAxis) → l
22. Point(k) → K
23. Point(k) → M
24. Point(l) → N
25. Point(l) → O
26. Segment(O, N) → m
27. Segment(M, K) → n
28. Circle(M, 1.2) → q
29. Vector((0, 0), (a, 0)) → u
30. Translate(L, u) → L'
31. Circle(L', 1.2) → r
32. Intersect(q, r, 2) → P
33. Segment(M, P) → p
34. Segment(L', P) → s
35. Circle(O, 1.2) → t
36. Intersect(r, t, 1) → Q
37. Segment(O, Q) → a_1
38. Segment(L', Q) → b_1
39. Translate(R, u) → R'
40. Circle(R', 0.2) → d_1
41. Segment(R', L') → c_1
42. Point(c_1) → S
43. Translate(T, u) → T'
44. Translate(U, u) → U'
45. Segment(S, T') → e_1
46. Segment(S, U') → f_1
47. Translate(W, u) → W'
48. Translate(V, u) → V'
49. Segment(T', W') → g_1
50. Segment(U', V') → h_1
51. Rotate(S, a / 4, S) → S'
52. Rotate(S', sin(a), S) → S''
53. Polygon(S, W', T') → poly1, t', s_1, w'
54. Rotate(S, sin((2 * a)), S'') → S'_1
55. Rotate(S, sin(a), S'') → S'_2
56. Rotate(W', sin(a), S'') → W''_1
57. Rotate(T', sin(a), S'') → T''_1
58. Polygon(S'_2, W''_1, T''_1) → poly1', t''_1, s'_2, w''_1
59. Polygon(V', U', S) → poly2, s_2, v', u'
60. Rotate(V', (-sin(a)), S'') → V''
61. Rotate(U', (-sin(a)), S'') → U''
62. Rotate(S, (-sin(a)), S'') → S'_3
63. Polygon(V'', U'', S'_3) → poly2', s'_3, v'', u''
64. Segment(W''_1, T''_1) → i_1
65. Segment(T''_1, S) → j_1
66. Segment(S, U'') → k_1
67. Segment(V'', U'') → l_1
68. Segment(U'', V'') → m_1
69. Point(p) → Z
70. Polygon(K, M, Z) → poly3, z_1, k_2, m_2
71. Rotate(S, (0.5 * sin((2 * a))), S'') → S'_4
72. Rotate(W', (0.5 * sin((2 * a))), S'') → W''
73. Rotate(T', (0.5 * sin((2 * a))), S'') → T''
74. Polygon(S'_4, W'', T'') → poly1'_1, t'', s'_4, w''
75. Point(a_1) → A_1
76. Polygon(O, N, A_1) → poly4, a_2, o, n_1
77. Point(c) → B_1
78. Sequence(Rotate[B_1, (π / 24 * n), A], n, 1, 49) → list1
79. Sequence(Segment[Element[list1, n], A], n, 1, 49) → list2
80. Sequence(Rotate[Element[list2, n], (-a), A], n, 1, 49) → list3
81. Circle((0, 1), 1) → p_1
82. Point(xAxis) → D_1
83. Segment(C_1, D_1) → q_1
84. Point(d_1) → E_1