GeoGebra椭圆的射影几何构造与性质探究

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → E_1
2. Mirror(F_1, yAxis) → G_1
3. Mirror(FF, yAxis) → FF'
4. Polygon(FF', FF, F_1, G_1) → poly5, ff', ff, f_2, g_2
5. Mirror(D, A) → D'
6. Mirror(B, A) → B'
7. Polygon(D', B', D, B) → poly1, d', b', d, b_1
8. PointIn(poly1) → L
9. Midpoint(d) → F
10. Segment(F, D) → c
11. Point(c) → G
12. Line(G, b') → e
13. Intersect(e, d') → H
14. Polygon(R, Q, H, G) → poly3, r, q, h, g
15. Point(b') → E
16. Segment(L, E) → t
17. Intersect(t, e) → U
18. Segment(E, O) → f
19. Line(U, f) → c_1
20. Point(f) → P
21. Segment(P, L) → i
22. Intersect(c_1, i) → V
23. Line(V, q) → r_2
24. Intersect(r_2, h) → B_2
25. Segment(V, B_2) → t_2
26. Mirror(H, D') → H'
27. Midpoint(D', F) → I
28. Midpoint(d') → J
29. PointIn(poly1) → K
30. PointIn(poly1) → M
31. PointIn(poly1) → N
32. Polygon(L, N, M, K) → poly2, l, n, m, k
33. Segment(P, N) → j
34. Segment(P, M) → p
35. Segment(P, K) → s
36. Segment(K, E) → a_1
37. Intersect(a_1, e) → S
38. Intersect(e, h) → T
39. Line(S, f) → d_1
40. Intersect(d_1, s) → W
41. Segment(N, E) → e_1
42. Segment(M, E) → f_1
43. Intersect(e_1, e) → A_1
44. Intersect(f_1, e) → B_1
45. Line(A_1, f) → g_1
46. Intersect(j, g_1) → C_1
47. Line(B_1, f) → h_1
48. Intersect(h_1, p) → D_1
49. Polygon(V, C_1, D_1, W) → poly4, v_1, c_2, d_2, w_1
50. Segment(P, E) → i_1
51. Segment(D, E) → j_1
52. Line(C_1, V) → l_1
53. Intersect(l_1, r) → J_1
54. Intersect(l_1, h) → K_1
55. Segment(R, J_1) → m_1
56. Segment(G, K_1) → n_1
57. Line(D_1, W) → q_1
58. Intersect(r, q_1) → L_1
59. Intersect(h, n_1) → M_1
60. Intersect(q_1, h) → N_1
61. Segment(R, L_1) → r_1
62. Line(V, W) → a_2
63. Intersect(g, a_2) → O_1
64. Line(C_1, D_1) → e_2
65. Intersect(e_2, g) → P_1
66. Intersect(l_1, q_1) → U_1
67. Segment(N_1, U_1) → k_2
68. Line(W, r) → k_1
69. Line(W, g) → p_1
70. Intersect(k_1, g) → I_1
71. Intersect(p_1, h) → Q_1
72. Segment(I_1, G) → t_1
73. Segment(G, Q_1) → i_2
74. Line(D_1, g) → s_1
75. Line(D_1, r) → b_2
76. Intersect(b_2, g) → R_1
77. Intersect(h, poly1) → S_1, S_2
78. Intersect(s_1, h) → T_1
79. Segment(R_1, D_1) → h_2
80. Segment(D_1, T_1) → j_2
81. Line(WH, ff') → l_2
82. Line(WL, g_2) → m_2
83. Intersect(l_2, m_2) → V_1
84. Line(DH, ff') → n_2
85. Line(DL, g_2) → p_2
86. Intersect(p_2, n_2) → W_1
87. Line(V, r) → q_2
88. Intersect(q_2, poly3) → Z_1, A_2
89. Segment(V, A_2) → s_2
90. Line(VD, g_2) → a_3
91. Line(VH, ff') → b_3
92. Intersect(a_3, b_3) → C_2
93. Line(C_1, r) → c_3
94. Line(C_1, g) → d_3
95. Intersect(h, poly1) → D_2, D_3
96. Intersect(h, poly1) → E_2, E_3
97. Intersect(c_3, q) → F_2
98. Intersect(h, poly1) → G_2, G_3
99. Intersect(d_3, h) → H_2
100. Segment(F_2, C_1) → e_3
101. Segment(C_1, H_2) → f_3
102. Line(CH, ff') → g_3
103. Line(CL, g_2) → h_3
104. Intersect(g_3, h_3) → I_2
105. Polygon(C_2, V_1, W_1, I_2) → poly6, c_4, v_2, w_2, i_3
106. PointIn(poly1) → L_2
107. Conic(L_2, K, L, N, M) → k_3
108. Segment(L_2, P) → j_3
109. Segment(E, L_2) → l_3
110. Intersect(l_3, poly1) → M_2, M_3
111. Intersect(l_3, poly1) → N_2, N_3
112. Intersect(e, l_3) → O_2
113. Line(O_2, g) → m_3
114. Intersect(m_3, j_3) → P_2
115. Conic(W, V, C_1, D_1, P_2) → p_3
116. Line(P_2, r) → n_3
117. Line(P_2, g) → q_3
118. Intersect(n_3, g) → Q_2
119. Intersect(q_3, h) → R_2
120. Segment(P_2, R_2) → r_3
121. Segment(P_2, Q_2) → s_3
122. Conic(ZH, V_1, C_2, I_2, W_1) → t_3
123. Line(P, A) → f_4
124. Point(f_4) → C
125. Sphere(C - (0, 0.13, -0.05), 0.3) → o_1
126. Sphere(C, 0.2) → u_1
127. Sequence(R + (i * Vector[R, Q]), i, 0, 1, 1 / o_2) → l1
128. Sequence(G + (i * Vector[R, Q]), i, 0, 1, 1 / o_2) → l2
129. Sequence(G + (i * Vector[G, R]), i, 0, 1, 1 / u_2) → l3
130. Sequence(H + (i * Vector[G, R]), i, 0, 1, 1 / u_2) → l4
131. Sequence(Segment[Element[l3, i], Element[l4, i]], i, 1, Length[l3]) → l5
132. Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, Length[l1]) → l6