方程C：圆锥曲线与旋转逻辑的交互探究

GeoGebra 命令及参数

1. Angle(angle_c, angle_b, angle_a) → anglemeasure
2. Polygon(C_1, C_2, 4) → x_c, c_1, c_2, c_3, c_4, C_3, C_4
3. Polygon(A_1, A_2, 4) → x_a, a_1, a_2, a_4, a_3, A_3, A_4
4. Polygon(P_1, P_2, 4) → x_P, p_1, p_2, p_4, p_3, P_3, P_4
5. Point(xAxis) → foot1
6. Segment(fulcrum, foot1) → leg_b
7. Point(xAxis) → foot2
8. Segment(fulcrum, foot2) → leg_a
9. Circle(fulcrum, 4) → circle
10. Line(fulcrum, xAxis) → parallel
11. Intersect(circle, parallel, 2) → balance1
12. Intersect(circle, parallel, 1) → balance2
13. Segment(balance1, balance2) → balance
14. Segment(angle_a, angle_b) → anglesegment_a
15. Segment(angle_b, angle_c) → anglesegment_b
16. Rotate(balance1, tip, fulcrum) → balance1'
17. Rotate(balance2, tip, fulcrum) → balance2'
18. Segment(balance1', balance2') → balance'
19. PointIn(x_c) → A
20. PointIn(x_P) → C
21. PointIn(x_a) → P
22. If(equal > tipequal, ">", If[equal < tipequal, "<", "="]) → sign
23. Circle(O, 0.25) → o
24. Circle(D, 0.25) → d
25. Polygon(Q_1, Q_2, 4) → x_Q, q_3, q_1, q_2, q_4, Q_3, Q_4
26. PointIn(x_Q) → Q
27. Polygon(F_1, F_2, 4) → x_F, f_2, f_1, f_3, f_4, F_3, F_4
28. Polygon(E_1, E_2, 4) → x_E, e_2, e_1, e_3, e_4, E_4, E_3
29. PointIn(x_F) → E
30. PointIn(x_E) → F
31. Polygon(H_1, H_2, 4) → x_H, h_2, h_1, h_3, h_4, H_3, H_4
32. Polygon(G_1, G_2, 4) → x_G, g_2, g_1, g_3, g_4, G_3, G_4
33. PointIn(x_H) → H
34. PointIn(x_G) → G
35. Polygon(J_1, J_2, 4) → x_J, j_2, j_1, j_3, j_4, J_3, J_4
36. Polygon(I_1, I_2, 4) → x_I, i_2, i_1, i_3, i_4, I_3, I_4
37. PointIn(x_J) → I
38. PointIn(x_I) → J
39. Circle(K, 0.25) → k
40. Circle(L, 0.25) → l
41. Circle(S, 0.25) → s
42. Circle(U, 0.25) → u
43. Circle(R, 0.25) → r
44. Circle(T, 0.25) → t
45. Circle(W, 0.25) → w
46. Circle(V, 0.25) → v
47. Circle(Y, 0.25) → y_1
48. Circle(X, 0.25) → x_1
49. Circle(Z2, 0.25) → z2
50. Circle(Z, 0.25) → z
51. Polygon(M_1, M_2, 4) → x_M, m_2, m_1, m_3, m_4, P_7, P_8
52. PointIn(x_M) → M
53. Polygon(C'_1, C'_2, 4) → x_{C'}, c'_2, c'_1, c'_3, c'_4, Q_7, Q_8
54. PointIn(x_{C'}) → C'
55. Polygon(A'_1, A'_2, 4) → x_{A'}, a'_2, a'_1, a'_3, a'_4, P_{11}, P_{12}
56. PointIn(x_{A'}) → A'
57. Polygon(D'_1, D'_2, 4) → x_{D'}, d'_2, d'_1, d'_3, d'_4, Q_{12}, Q_{13}
58. PointIn(x_{D'}) → D'
59. Polygon(B'_1, B'_2, 4) → x_{B'}, b'_2, b'_1, b'_3, b'_4, P_{15}, P_{16}
60. PointIn(x_{B'}) → B'
61. Polygon(E'_1, E'_2, 4) → x_{E'}, e'_2, e'_1, e'_3, e'_4, Q_{17}, Q_{18}
62. PointIn(x_{E'}) → E'
63. Circle(N, 0.25) → n
64. Circle(B, 0.25) → b
65. Circle(J2, 0.25) → j'
66. Circle(L2, 0.25) → l'
67. Circle(K2, 0.25) → k'
68. Circle(M2, 0.25) → m'
69. Polygon(I'_2, I'_1, 4) → x_2, i'_2, i'_1, i'_3, i'_4, P_6, P_{10}
70. PointIn(x_2) → I'
71. Polygon(G'_2, G'_1, 4) → x_3, g'_2, g'_1, g'_3, g'_4, Q_6, Q_{10}
72. PointIn(x_3) → G'
73. Polygon(F'_2, F'_1, 4) → x_4, f'_2, f'_1, f'_3, f'_4, P_5, P_9
74. PointIn(x_4) → F'
75. Polygon(H'_2, H'_1, 4) → x_5, h'_2, h'_1, h'_3, h'_4, Q_5, Q_9
76. PointIn(x_5) → H'
77. Textfield(unknown) → answer