近似值的探索：π的近似值

GeoGebra 命令及参数

1. SpeechBubbleLeft(PBubblePiaStart, 10.5, 2.4) → bubble1
2. SpeechBubbleLeft(PBubblePia, 13, 2.2) → bubble2
3. Circle(KreisMittelpunkt, B) → c
4. Segment(A, B) → f
5. SpeechBubbleLeft(PBubblePia, 10, 1.2) → bubble3
6. Segment(C, D) → g
7. Segment(D, E) → h
8. Segment(E, F) → i
9. Segment(F, C) → j
10. Segment(G, H) → k
11. Segment(H, I) → l
12. Segment(I, J) → m
13. Segment(J, G) → n
14. CircumcircleArc(K, L, M) → d
15. CircumcircleArc(N, O, P) → e
16. Point(d) → Q
17. Vector(Q, R) → u
18. Point(e) → S
19. Vector(S, T) → v
20. Segment(U, V) → p
21. SpeechBubbleLeft(PBubblePia - (0, 0.8), 12.2, 3.2) → bubble4
22. Textfield(input1) → InputBox1
23. SpeechBubbleLeft(PBubblePia, 8, 1) → bubble5
24. Textfield(input2) → InputBox2
25. Textfield(input3) → InputBox3
26. SpeechBubbleLeft(PBubblePia, 10.5, 1.8) → bubble6
27. Sequence(Rotate[B, (360 / 6 * i°), KreisMittelpunkt], i, 1, 6) → l1
28. Point(l1) → W
29. Point(l1) → Z
30. Segment(W, Z) → q
31. Point(l1) → A_1
32. Segment(Z, A_1) → r
33. Point(l1) → B_1
34. Segment(A_1, B_1) → s
35. Point(l1) → C_1
36. Segment(B_1, C_1) → t
37. Point(l1) → D_1
38. Segment(C_1, D_1) → a
39. Segment(D_1, W) → b
40. Sequence(Rotate[E_1, (360 / 6 * i°), KreisMittelpunkt], i, 1, 6) → l2
41. Point(l2) → F_1
42. Segment(E_1, F_1) → f_1
43. Point(l2) → G_1
44. Segment(F_1, G_1) → g_1
45. Point(l2) → H_1
46. Segment(G_1, H_1) → h_1
47. Point(l2) → I_1
48. Segment(H_1, I_1) → i_1
49. Point(l2) → J_1
50. Segment(I_1, J_1) → j_1
51. Segment(J_1, E_1) → k_1
52. CircumcircleArc(K_1, L_1, M_1) → c_1
53. Point(c_1) → N_1
54. Vector(N_1, O_1) → w
55. CircumcircleArc(P_1, Q_1, R_1) → d_1
56. Point(d_1) → S_1
57. Vector(S_1, T_1) → u_1
58. SpeechBubbleLeft(PBubblePia, 12.7, 1.8) → bubble7
59. SpeechBubbleLeft(PBubblePia, 8.4, 1.3) → bubble8
60. Textfield(input4) → InputBox4
61. Textfield(input5) → InputBox5
62. SpeechBubbleLeft(PBubblePia, 10.4, 2) → bubble9
63. SpeechBubbleLeft(PBubblePia, 12.8, 2) → bubble10
64. Circle(Kreis1, Kreisrand1) → e_1
65. Circle(Kreis2, Kreisrand2) → e_{2}
66. Circle(Kreis3, Kreisrand3) → e_{3}
67. Sequence(Rotate[Kreisrand1, (360 / 12 * i°), Kreis1], i, 1, 12) → l3
68. Sequence(Rotate[Kreisrand2, (360 / 24 * i°), Kreis2], i, 1, 24) → l4
69. Sequence(Rotate[Kreisrand3, (360 / 96 * i°), Kreis3], i, 1, 96) → l5
70. Join({Sequence[Segment[l3(i - 1), l3(i)], i, 2, 12], {Segment[l3(12), l3(1)]}}) → l6
71. Join({Sequence[Segment[l4(i - 1), l4(i)], i, 2, 24], {Segment[l4(24), l4(1)]}}) → l7
72. Join({Sequence[Segment[l5(i - 1), l5(i)], i, 2, 96], {Segment[l5(96), l5(1)]}}) → l8
73. Sequence(Rotate[Kreisrand1_2, (360 / 12 * i°), Kreis1], i, 1, 12) → l9
74. Join({Sequence[Segment[l9(i - 1), l9(i)], i, 2, 12], {Segment[l9(12), l9(1)]}}) → l10
75. Sequence(Rotate[Kreisrand2_2, (360 / 24 * i°), Kreis2], i, 1, 24) → l11
76. Join({Sequence[Segment[l11(i - 1), l11(i)], i, 2, 24], {Segment[l11(24), l11(1)]}}) → l12
77. Sequence(Rotate[Kreisrand3_2, (360 / 96 * i°), Kreis3], i, 1, 96) → l13
78. Join({Sequence[Segment[l13(i - 1), l13(i)], i, 2, 96], {Segment[l13(96), l13(1)]}}) → l14
79. SpeechBubbleLeft(PBubblePiaEnde, 11.5, 1.8) → bubble11
80. SpeechBubbleLeft(PBubblePiaEnde, 11.5, 1.8) → bubbleColor
81. SpeechBubbleLeft(PBubblePia, 13.5, 1.7) → bubble45
82. Circle(Kreis4, Kreisrand4) → e_{4}
83. Circle(Kreis5, Kreisrand5) → e_{5}
84. Sequence(Rotate[Kreisrand5, (360 / 4 * i°), Kreis5], i, 1, 12) → l15
85. Join({Sequence[Segment[l15(i - 1), l15(i)], i, 2, 12], {Segment[l15(12), l15(1)]}}) → l16
86. Sequence(Rotate[Kreisrand5_{1}, (360 / 4 * i°), Kreis5], i, 1, 4) → l17
87. Sequence(Rotate[Kreisrand4, (360 / 6 * i°), Kreis4], i, 1, 6) → l19
88. Join({Sequence[Segment[l19(i - 1), l19(i)], i, 2, 6], {Segment[l19(6), l19(1)]}}) → l20
89. Sequence(Rotate[Kreisrand4_{1}, (360 / 6 * i°), Kreis4], i, 1, 6) → l21
90. Join({Sequence[Segment[l21(i - 1), l21(i)], i, 2, 6], {Segment[l21(6), l21(1)]}}) → l22
91. Segment(U_1, V_1) → l_1
92. Segment(V_1, W_1) → m_1
93. Segment(W_1, Z_1) → n_1
94. Segment(Z_1, U_1) → p_1
95. Angle(B_1, KreisMittelpunkt, U) → α
96. Textfield(input2_1) → InputBox2_1
97. Textfield(input3_1) → InputBox3_1
98. Textfield(input4_1) → InputBox4_1
99. Textfield(input5_1) → InputBox5_1
100. Segment(I, J) → m_{neu}
101. Segment(B, KreisMittelpunkt) → f_{neu}
102. Segment(KreisMittelpunkt, U) → p_{neu}