3.2 瓷砖拼贴：向量平移与对称变换的几何探究

GeoGebra 命令及参数

1. Line(A, B) → b
2. Circle(A, a) → c
3. Intersect(c, b, 2) → C
4. Polygon(A, C, 4) → poly1, d, e, f, g, D, E
5. Point(b) → F
6. Vector(A, F) → u
7. Translate(A, u) → A'
8. Translate(C, u) → C'
9. Translate(D, u) → D'
10. Translate(E, u) → E'
11. Polygon(A', C', D', E') → poly1', a', c', d', e'
12. Translate(A', u) → A''
13. Translate(C', u) → C''
14. Translate(D', u) → D''
15. Translate(E', u) → E''
16. Polygon(A'', C'', D'', E'') → poly1'', a'', c'', d'', e''
17. Translate(A'', u) → A'''
18. Translate(C'', u) → C'''
19. Translate(D'', u) → D'''
20. Translate(E'', u) → E'''
21. Translate(A''', u) → G
22. Translate(C''', u) → H
23. Translate(D''', u) → I
24. Translate(E''', u) → J
25. Translate(G, u) → G'
26. Translate(H, u) → H'
27. Translate(I, u) → I'
28. Translate(J, u) → J'
29. Point(e') → S
30. Point(d'') → T
31. Point(e'') → U
32. Vector(A, L_1) → v_1
33. Translate(A, v_1) → A'_1
34. Translate(C, v_1) → C'_1
35. Translate(D, v_1) → D'_1
36. Translate(E, v_1) → E'_1
37. Polygon(A'_1, C'_1, D'_1, E'_1) → poly1'_1, a'_1, c'_1, d'_1, e'_1
38. Translate(A', v_1) → A''_1
39. Translate(C', v_1) → C''_1
40. Translate(D', v_1) → D''_1
41. Translate(E', v_1) → E''_1
42. Polygon(A''_1, C''_1, D''_1, E''_1) → poly1''_1, a''_1, c''_1, d''_1, e''_1
43. Midpoint(e'_1) → M_1
44. Midpoint(c'_1) → N_1
45. Midpoint(d'_1) → O_1
46. Midpoint(a'_1) → P_1
47. Midpoint(O_1, P_1) → Q_1
48. Segment(M_1, Q_1) → d_1
49. Point(d_1) → R_1
50. Midpoint(e''_1) → S_1
51. Midpoint(d''_1) → T_1
52. Midpoint(a''_1) → U_1
53. Midpoint(T_1, U_1) → V_1
54. Mirror(R_1, Q_1) → Z_1
55. Polygon(O_1, R_1, P_1, Z_1) → poly10, o_1, r_1, p_1, z_1
56. Segment(C, E) → q_1
57. Segment(A, D) → s_1
58. Segment(A'', D'') → b_2
59. Segment(P_1, O_1) → c_2
60. Segment(A''_1, D''_1) → d_2
61. Segment(E''_1, C''_1) → e_2
62. Segment(M_1, N_1) → f_2
63. Midpoint(f) → K
64. Midpoint(g) → M
65. Midpoint(d) → N
66. Midpoint(e) → O
67. Polygon(K, M, N, O) → poly3, k, m, n, o
68. Midpoint(d') → P
69. Midpoint(a') → R
70. OrthogonalLine(S, e') → p
71. OrthogonalLine(T, b_2) → q
72. OrthogonalLine(U, b_2) → r
73. Intersect(c', p) → Q
74. Intersect(a'', r) → V
75. Intersect(q, c'') → W
76. Polygon(S, P, Q, R) → poly4, s, p_2, q_2, r_2
77. Polygon(U, T, W, V) → poly5, u_1, t, w, v
78. Segment(V_1, E''_1) → c_1
79. Segment(P, R) → e_1
80. Segment(K, N) → l_1
81. Segment(O, M) → m_1
82. Vector(A, B_2) → n_1
83. Translate(A, n_1) → A'_2
84. Translate(C, n_1) → C'_2
85. Translate(D, n_1) → D'_2
86. Translate(E, n_1) → E'_2
87. Polygon(A'_2, C'_2, D'_2, E'_2) → poly1'_2, a'_2, c'_2, d'_2, e'_2
88. Translate(A', n_1) → A''_2
89. Translate(C', n_1) → C''_2
90. Translate(D', n_1) → D''_2
91. Translate(E', n_1) → E''_2
92. Polygon(A''_2, C''_2, D''_2, E''_2) → poly1''_2, a''_3, c''_2, d''_3, e''_2
93. Translate(A'', n_1) → A'''_1
94. Translate(C'', n_1) → C'''_1
95. Translate(D'', n_1) → D'''_1
96. Translate(E'', n_1) → E'''_1
97. Polygon(A'''_1, C'''_1, D'''_1, E'''_1) → poly1'''_1, a'''_1, c'''_1, d'''_1, e'''_1
98. Point(d'_2) → D_2
99. Point(e'_2) → H_2
100. Midpoint(E'_2, C'_2) → I_2
101. Midpoint(E''_2, C''_2) → J_2
102. Point(d''_3) → K_2
103. Point(d'''_1) → L_2
104. Point(e'''_1) → M_2
105. Point(a'''_1) → N_2
106. Point(c'''_1) → P_2
107. Mirror(D_2, I_2) → O_2
108. Mirror(H_2, I_2) → Q_2
109. Rotate(K_2, 90°, J_2) → R_2
110. Mirror(K_2, J_2) → S_2
111. Polygon(D_2, H_2, O_2, Q_2) → poly11, d_3, h_2, o_2, q_3
112. Mirror(R_2, J_2) → T_2
113. Polygon(K_2, R_2, S_2, T_2) → poly12, k_2, r_3, s_2, t_2
114. Polygon(L_2, M_2, N_2, P_2) → poly13, l_2, m_2, n_2, p_3
115. Angle(Q_2, I_2, H_2) → γ
116. Angle(T_2, J_2, K_2) → δ
117. Point(d''_1) → L
118. Mirror(L, d_2) → L'
119. Mirror(L, e_2) → L'_1
120. Mirror(L', e_2) → L''
121. Polygon(L, L', L'', L'_1) → poly2, l, l', l'', l'_1
122. Angle(D''_1, V_1, A''_1) → α
123. Intersect(l_1, m_1) → Z
124. Angle(O, Z, K) → β
125. Angle(Z_1, Q_1, R_1) → ε