虚平面：三维空间中的几何构造与变换

GeoGebra 命令及参数

1. Point(xAxis) → A
2. Segment(A, B) → f
3. Point(xAxis) → C
4. Segment(C, D) → g
5. Segment(D, B) → h
6. Segment(A, C) → i
7. Point(i) → E
8. Point(h) → F
9. Segment(E, F) → j
10. Segment(G, F) → k
11. Point(yAxis) → H
12. Segment(G, H) → l
13. Segment(H, E) → m
14. Point(h) → I
15. Polygon(H, E, F, G) → q1, h_1, e, f_1, g_1
16. Polygon(B, D, C, A) → q2, b, d, c, a
17. Mirror(F, j) → F'
18. Intersect(p, yAxis, 1) → J
19. Vector(K, L) → u
20. Translate(B, u) → B'
21. Translate(D, u) → D'
22. Translate(C, u) → C'
23. Translate(A, u) → A'
24. Polygon(B', D', C', A') → q2', b', d', c', a'
25. Rotate(B, 90°, E) → B'_1
26. Rotate(D, 90°, E) → D'_1
27. Rotate(C, 90°, E) → C'_1
28. Rotate(A, 90°, E) → A'_1
29. Polygon(B'_1, D'_1, C'_1, A'_1) → q2'_1, b'_1, d'_1, c'_1, a'_1
30. Rotate(B, (-(90°)), E) → B'_2
31. Rotate(D, (-(90°)), E) → D'_2
32. Rotate(C, (-(90°)), E) → C'_2
33. Rotate(A, (-(90°)), E) → A'_2
34. Polygon(B'_2, D'_2, C'_2, A'_2) → q2'_2, b'_2, d'_2, c'_2, a'_2
35. Mirror(B'_2, yAxis) → M
36. Mirror(D'_2, yAxis) → N
37. Mirror(C'_2, yAxis) → O
38. Mirror(A'_2, yAxis) → P
39. Polygon(M, N, O, P) → q3, m_1, n, o, p_1
40. Mirror(B'_1, yAxis) → Q
41. Mirror(D'_1, yAxis) → R
42. Mirror(C'_1, yAxis) → S
43. Mirror(A'_1, yAxis) → T
44. Polygon(Q, R, S, T) → q4, q, r, s, t
45. Point(t) → V
46. Line(V, t) → i_1
47. Point(r) → Z
48. Line(Z, r) → j_1
49. Point(i_1) → U
50. Point(j_1) → W
51. Segment(U, W) → k_1
52. Polygon(V, U, W, Z) → q5, v, u_1, w, z_1
53. Segment(A_1, B_1) → l_1
54. Segment(B_1, C_1) → n_1
55. Polygon(C_1, A_1, B_1) → t1, b_1, c_1, a_1
56. Point(yAxis) → D_1
57. Polygon(D_1, J, E_1, F_1) → q6, d_1, j_2, e_1, q_1
58. Rotate(D_1, (-(180°)), J) → G_1
59. Rotate(J, (-(180°)), J) → J'
60. Rotate(E_1, (-(180°)), J) → H_1
61. Rotate(F_1, (-(180°)), J) → I_1
62. Polygon(G_1, J', H_1, I_1) → q6', r_1, j', s_1, t_1
63. Vector(J_1, K_1) → v_1
64. Translate(G_1, v_1) → L_1
65. Translate(J', v_1) → J''
66. Translate(H_1, v_1) → M_1
67. Translate(I_1, v_1) → N_1
68. Polygon(L_1, J'', M_1, N_1) → q6'', f_2, j'', g_2, h_2
69. Polygon(O_1, P_1, Q_1, R_1) → q7, o_1, i_2, k_2, l_2
70. Point(Circle[E, 1]) → S_1
71. Segment(E, S_1) → m_2
72. Point(Circle[E, -1]) → T_1
73. Segment(E, T_1) → n_2
74. Rotate(E, 180°, E) → E'
75. Rotate(S_1, 180°, E) → U_1
76. Segment(E', U_1) → p_2
77. Rotate(O_1, 180°, J) → V_1
78. Rotate(P_1, 180°, J) → W_1
79. Rotate(Q_1, 180°, J) → Z_1
80. Rotate(R_1, 180°, J) → A_2
81. Polygon(V_1, W_1, Z_1, A_2) → q7', q_2, w_1, r_2, a_2
82. Vector(B_2, C_2) → u_2
83. Translate(V_1, u_2) → D_2
84. Translate(W_1, u_2) → E_2
85. Translate(Z_1, u_2) → F_2
86. Translate(A_2, u_2) → G_2
87. Polygon(D_2, E_2, F_2, G_2) → q7'', d_2, e_2, s_2, t_2
88. Vector(H_2, I_2) → v_2
89. Translate(B, v_2) → B'_3
90. Translate(D, v_2) → D'_3
91. Translate(C, v_2) → C'_3
92. Translate(A, v_2) → A'_3
93. Polygon(B'_3, D'_3, C'_3, A'_3) → q2'_3, b'_3, d'_3, c'_3, a'_3
94. Intersect(d', c') → J_2
95. Segment(J_2, K_2) → b_2
96. Segment(J_2, L_2) → c_2
97. Segment(J_2, M_2) → f_3
98. Point(p_2) → N_2
99. Point(m_2) → O_2
100. Angle(c', i_2) → α
101. Segment(J, O_2) → g_3
102. Angle(g_3, m_2) → β