平行四边形外接等边三角形的动态几何现象（GoGeometry Action 45）

GeoGebra 命令及参数

1. Rotate(B, a°, A) → B'
2. Angle(B, A, B') → α
3. Ray(A, B) → f
4. Ray(A, B') → g
5. Line(B, g) → h
6. Point(g) → C
7. Line(C, f) → i
8. Intersect(h, i) → D
9. Segment(C, D) → j
10. Segment(A, B) → k
11. Segment(B, D) → l
12. Segment(A, C) → m
13. Min(m, k) → b
14. Circle(C, (0.2 * b)) → d
15. Circle(A, (0.2 * b)) → e
16. Circle(B, (0.2 * b)) → p
17. Circle(D, (0.2 * b)) → c
18. Intersect(e, k, 1) → E
19. Intersect(e, m, 1) → F
20. Intersect(p, k, 1) → G
21. Intersect(p, l, 1) → H
22. Intersect(d, g, 2) → I
23. Ray(C, I) → q
24. Intersect(c, h, 2) → J
25. Ray(D, J) → r
26. Intersect(c, i, 2) → K
27. Ray(D, K) → s
28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
29. Segment(A, A') → t
30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
31. CircleSector(A, E, E') → c_1
32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
33. Vector(A, A'_1) → u
34. Translate(c_1, u) → d_1
35. Segment(A, A'_1) → f_1
36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
37. Vector(C, C') → v
38. Translate(d_1, v) → e_1
39. Segment(C, C') → g_1
40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
41. Segment(D, D') → h_1
42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
44. Vector(A, A'_2) → w
45. Translate(A, w) → A'_3
46. Translate(A', w) → A''
47. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
48. Vector(A, A'_4) → u_1
49. Translate(A, u_1) → A'_5
50. Translate(A'_1, u_1) → L
51. Rotate(B, π / 3, D) → B'_1
52. Rotate(D, π / 3, C) → D'_1
53. Rotate(A, π / 3, B) → A'_6
54. Rotate(C, π / 3, A) → C'_1
55. Rotate(D, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → D'_2
56. Rotate(D', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → D''
57. Segment(D'_2, D'') → i_1
58. Rotate(C, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → C'_2
59. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → C''
60. Segment(C'_2, C'') → j_1
61. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → A'_7
62. Rotate(A'_1, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → M
63. Segment(A'_7, M) → k_1
64. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A'_8
65. Rotate(A', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A''_1
66. Segment(A'_8, A''_1) → t'
67. Rotate(D, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → D'_3
68. Rotate(D', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → D''_1
69. Segment(D'_3, D''_1) → l_1
70. Rotate(C, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → C'_3
71. Rotate(C', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → C''_1
72. Segment(C'_3, C''_1) → m_1
73. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → A'_9
74. Rotate(A'_1, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → N
75. Segment(A'_9, N) → n_1
76. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → A'_{10}
77. Rotate(A', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → A''_2
78. Segment(A'_{10}, A''_2) → t'_1
79. Polygon(B, B'_1, D) → poly2, d_3, b_2, b'_1
80. Polygon(B, A, A'_6) → poly3, a'_6, b_3, a_2
81. Polygon(A, C, C'_1) → poly4, c'_1, a_3, c_3
82. Polygon(C, D, D'_1) → poly5, d'_1, c_4, d_4
83. Dilate(A'_6, If[8 < o ≤ 9, 9 - o, 0], B'_1) → O
84. Segment(A'_6, O) → p_1
85. Dilate(B'_1, If[9 < o ≤ 10, 10 - o, 0], D'_1) → P
86. Segment(B'_1, P) → q_1
87. Dilate(A'_6, If[10 < o ≤ 11, 11 - o, 0], C'_1) → Q
88. Vector(A'_6, Q) → v_1
89. Translate(A'_6, v_1) → R
90. Translate(O, v_1) → O'
91. Segment(R, O') → r_1
92. Dilate(B'_1, If[11 < o ≤ 12, 12 - o, 0], A'_6) → S
93. Vector(B'_1, S) → w_1
94. Translate(B'_1, w_1) → T
95. Translate(P, w_1) → P'
96. Segment(T, P') → s_1