用复数 i 的几何构造近似圆周率 π

GeoGebra 命令及参数

1. Semicircle(C, D) → c
2. Semicircle(D, C) → d
3. Segment(A, D) → a
4. Circle(A, 1) → f
5. Semicircle(E, F) → r
6. Semicircle(F, E) → g
7. Polygon(B, A, C, G) → poly1, b_1, a_1, c_1, g_1
8. Vector((1.414213562373095, 1.414213562373095)) → u_3
9. Vector((1.79, 0.89)) → v
10. Segment(G, B) → e
11. Segment(G, J) → h
12. Segment(G, K) → i
13. Angle(B, G, K) → α_u
14. Angle(B, G, J) → β_v
15. Vector((0.89, 1.79)) → w
16. Segment(G, L) → j
17. Angle(B, G, L) → δ_w
18. Angle(J, G, L) → Δ_v
19. Circle(G, K) → k
20. Point(r) → N
21. Point(g) → M
22. Segment(N, A) → p
23. Segment(A, M) → q
24. Segment(M, N) → s
25. Polygon(N, C, G, B, M) → poly2, n_1, c_2, g_2, b_2, m_1
26. Vector((2, 1)) → t
27. Vector((1, 2)) → u
28. Segment(G, N) → d_1
29. Segment(G, M) → e_1
30. Angle(M, G, N) → α_t
31. Segment(A, R) → k_1
32. Segment(A, Q) → l_1
33. Segment(Q, R) → p_1
34. Circle(A, S) → q_1
35. Distance(G, A) → distanceGA
36. Point(Circle[A, 3]) → T
37. Segment(A, T) → r_1
38. Point(Circle[G, 3]) → U
39. Segment(G, U) → s_1
40. Point(Circle[T, 2.8284271247461903]) → V
41. Segment(T, V) → t_1
42. Distance(G, Q) → distanceGQ
43. Distance(G, M) → distanceGM
44. Segment(G, M) → a_2
45. Segment(W, Z) → d_2
46. Vector(A_1, B_1) → u_2
47. Vector(C_1, D_1) → v_2
48. Distance(G, N) → distanceGN
49. Segment(G, N) → f_2
50. Distance(G, Q) → j_2
51. Point(k) → E_1
52. Point(k) → F_1
53. Distance(F_1, E_1) → distanceF1E1
54. Segment(E_1, F_1) → k_2
55. Point(k_2) → G_1
56. Point(s) → H_1
57. Distance(G_1, H_1) → distanceG1H1
58. Segment(G_1, H_1) → l_2
59. Segment(I_1, J_1) → m_2
60. Segment(K_1, L_1) → n_2
61. Segment(K_2, L_2) → n_3
62. Segment(K_3, L_3) → n_4
63. Segment(K_4, L_4) → n_5
64. Segment(K_5, L_5) → n_6
65. Segment(K_8, L_8) → n_9
66. Polygon(M_1, N_1, O_1, P_1) → poly3, m_3, n_{13}, o_2, p_2
67. Intersect(k, q_1, 1) → Q_1
68. Point(f_2) → R_1
69. Circle(Q_1, R_1) → q_2
70. Mirror(q_2, i) → r_2
71. Segment(S_1, T_1) → a_3
72. Segment(U_1, V_1) → b_3
73. Intersect(f_3, i, 1) → W_1
74. Point(f_3) → Z_1
75. Segment(W_1, Z_1) → d_3
76. Textfield(σ) → inputBox1
77. Point(f_3) → C_2
78. Point(f_3) → D_2
79. Vector(G, D_2) → v_3
80. Distance(G, D_2) → distanceGD2
81. Vector(E_2, F_2) → w_3
82. Mirror(N, p_1) → N'
83. Mirror(A, p_1) → A'
84. Segment(N', A') → p'
85. Mirror(A, p_1) → A'_1
86. Mirror(R, p_1) → R'
87. Segment(A'_1, R') → g_3
88. Mirror(A, p_1) → A'_2
89. Mirror(M, p_1) → M'
90. Segment(A'_2, M') → q'
91. Mirror(A, p_1) → A'_3
92. Mirror(Q, p_1) → Q'
93. Segment(A'_3, Q') → h_3
94. Segment(G, D_2) → i_3
95. Slope(i_3) → m_4
96. Point(p_3) → G_2
97. Distance(G, G_2) → distanceGG2
98. Vector(G, G_2) → j_3
99. Segment(G, G_2) → l_3
100. Angle(K, G, G_2) → α
101. Point(q_3) → H_2
102. Point(s_3) → I_2
103. Point(r_3) → J_2
104. Polygon(H_2, I_2, J_2, G) → poly4, h_4, i_4, j_4, g_4
105. Point(h_4) → M_2
106. Point(j_4) → N_2
107. Point(i_4) → O_2
108. Point(g_4) → P_2
109. Segment(O_2, M_2) → t_3
110. Segment(N_2, P_2) → a_4
111. Point(a_4) → Q_2
112. Point(t_3) → R_2
113. Segment(Q_2, R_2) → b_4
114. Point(i_4) → T_2