正五边形几何构造演示：GoGeometry 第 169 例动态作图

GeoGebra 命令及参数

1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
2. Segment(A, B) → k
3. Segment(B, C) → l
4. Segment(C, D) → m
5. Segment(D, E) → n
6. Segment(E, A) → p
7. Circle(E, D, C) → c
8. Center(c) → F
9. Rotate(A, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → A'
10. Rotate(B, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → B'
11. Segment(A', B') → k'
12. Rotate(B, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → B'_1
13. Rotate(C, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → C'
14. Segment(B'_1, C') → l'
15. Rotate(C, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → C'_1
16. Rotate(D, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → D'
17. Segment(C'_1, D') → m'
18. Rotate(D, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → D'_1
19. Rotate(E, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → E'
20. Segment(D'_1, E') → n'
21. Rotate(E, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → E'_1
22. Rotate(A, If[0 < a ≤ 1, ((a * 2) * π / 5), (2 * π / 5)], F) → A'_1
23. Segment(E'_1, A'_1) → p'
24. Rotate(D, If[2 < a ≤ 4, ((a - 2) * π), (2 * π)], F) → D'_2
25. CircleArc(F, D, D'_2) → d
26. CircleArc(F, D, E) → e
27. CircleArc(F, E, D) → q
28. Point(e) → G
29. Dilate(G, If[4 < a ≤ 5, 5 - a, 0], E) → G'
30. Dilate(G, If[5 < a ≤ 6, 6 - a, 0], A) → G'_1
31. Dilate(G, If[6 < a ≤ 7, 7 - a, 0], B) → G'_2
32. Dilate(G, If[7 < a ≤ 8, 8 - a, 0], C) → G'_3
33. Dilate(G, If[8 < a ≤ 9, 9 - a, 0], D) → G'_4
34. Segment(G, G') → r
35. Segment(G, G'_1) → s
36. Segment(G, G'_2) → t
37. Segment(G, G'_3) → b
38. Segment(G, G'_4) → f_1
39. Line(G, B) → g_1
40. Point(g_1) → H
41. Rotate(G, If[10 < a ≤ 11, (((-(a - 10)) * 3) * π / 5), (-3 * π / 5)], G) → G'_5
42. Rotate(G', If[10 < a ≤ 11, (((-(a - 10)) * 3) * π / 5), (-3 * π / 5)], G) → G''
43. Segment(G'_5, G'') → r'
44. Dilate(G, If[11 < a ≤ 12, 12 - a, 0], B) → G'_6
45. Vector(G, G'_6) → v
46. Translate(G, v) → G'_7
47. Translate(G'_4, v) → I
48. Segment(G'_7, I) → h_1
49. Rotate(G'_7, If[12 < a ≤ 13, (((-(a - 12)) * 2) * π / 5), (-2 * π / 5)], B) → J
50. Rotate(I, If[12 < a ≤ 13, (((-(a - 12)) * 2) * π / 5), (-2 * π / 5)], B) → I'
51. Segment(J, I') → i_1
52. OrthogonalLine(G'', t) → j_1
53. OrthogonalLine(I', i_1) → k_1
54. Point(j_1) → K
55. OrthogonalLine(K, j_1) → l_1
56. Intersect(l_1, k_1) → L
57. Circle(K, s) → c_1
58. Intersect(c_1, l_1, 1) → M
59. Dilate(G'', If[14 < a ≤ 15, 15 - a, 0], K) → G'''
60. Segment(G'', G''') → m_1
61. Angle(L, K, G'') → α
62. Angle(K, G'', G) → β
63. Dilate(K, If[15 < a ≤ 16, 16 - a, 0], M) → K'
64. Segment(K, K') → n_1
65. Vector(K, K') → w
66. Translate(G'', w) → G'''_1
67. Translate(G''', w) → N
68. Segment(G'''_1, N) → p_1
69. Dilate(M, If[16 < a ≤ 17, 17 - a, 0], L) → M'
70. Vector(M, M') → u_1
71. Translate(G'''_1, u_1) → O
72. Translate(N, u_1) → N'
73. Segment(O, N') → q_1
74. Segment(K', M') → r_1
75. Angle(I', L, K) → γ
76. Dilate(G, If[18 < a ≤ 19, 19 - a, 0], K) → G'_8
77. Vector(G, G'_8) → v_1
78. Translate(G, v_1) → G'_9
79. Translate(G'_1, v_1) → P
80. Segment(G'_9, P) → s'
81. Rotate(G'_9, If[18 < a ≤ 19, ((a - 18) * π / 5), π / 5], G'_9) → Q
82. Rotate(G'_9, If[18 < a ≤ 19, ((a - 18) * π / 5), π / 5], Q) → R
83. Rotate(P, If[18 < a ≤ 19, ((a - 18) * π / 5), π / 5], Q) → P'
84. Segment(R, P') → s''
85. Semicircle(G, K') → d_1
86. Center(d_1) → S
87. Rotate(G, If[19 < a ≤ 20, ((-(a - 19)) * π), (-π)], S) → G'_{10}
88. Vector(G, G'_{10}) → w_1
89. Translate(G, w_1) → G'_{11}
90. Translate(G'_3, w_1) → T
91. Segment(G'_{11}, T) → b'
92. Rotate(G'_{11}, If[19 < a ≤ 20, ((-(a - 19)) * π / 5), ((-π)) / 5], G'_{11}) → U
93. Rotate(T, If[19 < a ≤ 20, ((-(a - 19)) * π / 5), ((-π)) / 5], G'_{11}) → T'
94. Segment(U, T') → b''
95. Segment(G, A) → s_1
96. Segment(G, C) → t_1