轴对称小册子：探索对称变换与几何构造

GeoGebra 命令及参数

1. Midpoint(A, B) → C
2. Midpoint(E, C) → F
3. Midpoint(E, F) → J
4. Midpoint(J, E) → L_2
5. Mirror(J, E) → J'
6. Mirror(L_2, J') → L'_1
7. Mirror(J', L'_1) → J''
8. CircleArc(J'', A, B) → c
9. Point(c) → H
10. CircleArc(J'', H, B) → f_1
11. Line(A, B) → b
12. OrthogonalLine(C, b) → a
13. Midpoint(F, C) → G_2
14. OrthogonalLine(I, b) → d
15. Line(H, a) → e
16. Midpoint(J, E) → K
17. Vector(C, E) → u
18. Translate(J', u) → J''_1
19. Translate(A, u) → A'
20. Translate(B, u) → B'_1
21. Arc(Translate[Circle[J', A], u], A', B'_1) → c'
22. Midpoint(J', L'_1) → M_2
23. Translate(H, u) → N
24. Polygon(C, H, N, E) → poly1, c_1, h, n, e_1
25. Distance(A, H) → aa
26. Line(E, b) → f
27. Intersect(f, d) → O
28. Polygon(E, O, I, C) → poly3, e_3, o, i, c_3
29. Midpoint(I, C) → P
30. Mirror(B, P) → B'
31. Line(B', o) → g
32. Line(B, o) → j
33. Circle(I, B) → k
34. Intersect(d, o) → Q
35. Intersect(k, d) → R, S
36. Circle(O, B'_1) → p
37. Intersect(p, o) → T,
38. Line(T, f) → l
39. Line(S, b) → m
40. Intersect(l, g) → U
41. Intersect(m, g) → V
42. Intersect(m, j) → W
43. Midpoint(O, V) → Z
44. Midpoint(U, I) → B_1
45. Midpoint(G_2, V) → D_1
46. Line(D_1, c_1) → q
47. Intersect(q, h) → E_1
48. Midpoint(K, J) → G_1
49. Line(G_1, q) → s
50. Line(G_1, n) → r
51. Intersect(r, h) → F_1
52. Point(f_1) → G
53. Translate(G, u) → I_1
54. Polygon(E, I_1, G, C) → poly5, e_5, i_1, h_2, c_5
55. Midpoint(I_1, G) → J_1
56. Midpoint(T, I) → K_1
57. Midpoint(K_1, I) → L_1
58. Midpoint(G_2, L_1) → M_1
59. Segment(C, I) → g_1
60. Segment(C, G) → j_1
61. Segment(C, I) → b_1
62. CircleArc(J'', G, B) → k_1
63. Point(k_1) → L
64. Translate(L, u) → L'
65. Polygon(E, L', L, C) → poly6, l_1, m_1, n_1, p_1
66. CircleArc(J'', L, B) → q_1
67. Point(q_1) → M
68. Translate(M, u) → M'
69. Polygon(E, M', M, C) → poly7, r_1, s_1, t_1, a_2
70. Distance(A, G) → bb
71. Midpoint(M', M) → N_1
72. Polygon(N, E, C, H) → poly8, b_2, d_2, f_2, g_2
73. Midpoint(I_1, G) → H_1
74. Midpoint(e_1) → O_1
75. Midpoint(E, O_1) → P_1
76. Line(P_1, l_1) → a_1
77. Intersect(a_1, m_1) → Q_1
78. Midpoint(M, C) → R_1
79. Midpoint(M, R_1) → S_1
80. Midpoint(S_1, R_1) → T_1
81. Midpoint(S_1, T_1) → U_1
82. Midpoint(p_1) → V_1
83. Midpoint(M', E) → W_1
84. Midpoint(M', W_1) → Z_1
85. Midpoint(Z_1, W_1) → A_2
86. Midpoint(Z_1, A_2) → B_2
87. Point(p_1) → D_2
88. Intersect(p_1, l_1) → E_2
89. Polygon(D_2, E_2, O, I) → poly2, d_1, e_2, o_1, i_2
90. Midpoint(D_2, I) → C_2
91. Midpoint(C_2, I) → F_2
92. Midpoint(C_2, F_2) → H_2
93. Segment(O, I) → h_1
94. Segment(E_2, O) → c_2
95. Midpoint(C_2, H_2) → I_2
96. Point(q_1) → J_2
97. Segment(J_2, C) → j_2
98. Polygon(E, K_2, J_2, C) → q1, e_4, k_2, l_2, c_4
99. Midpoint(j_2) → N_2
100. Midpoint(N_2, J_2) → O_2
101. Midpoint(O_2, N_2) → P_2
102. Midpoint(P_2, N_2) → Q_2
103. Segment(K_2, J_2) → m_2
104. Intersect(e_4, c_4) → R_2
105. Segment(R_2, K_2) → n_2
106. Polygon(R_2, K_2, J_2, C) → q2, r_2, p_2, q_2, c_6
107. Sequence(Segment[Element[Marque, i], Element[Marque, i + 1]], i, 1, Length[Marque]) → Trait
108. PointIn(poly2) → S_2
109. Mirror(Trait, a_2) → Trait'
110. Rotate(Trait', 2, a_2) → Trait''