达兰贝尔球与抛物线

GeoGebra 命令及参数

1. InfiniteCone((0, 0, 0), zAxis, α) → a
2. Axes(a) → d, e, f
3. Rotate(f, (-α), yAxis) → lineOA
4. Point(lineOA) → A
5. Rotate(f, α, yAxis) → f'
6. Point(f') → B
7. Plane(A, B_1, B) → b
8. IntersectPath(b, a) → EllipseHyperbola
9. Axes(EllipseHyperbola) → i, j
10. AngularBisector(f', i) → b2, b1
11. Center(a) → O
12. Vector(O, B) → vOB
13. Angle(Vector[A, B], Vector[A, O]) → β
14. Vector(O, A) → vOA
15. Rotate(vOA, β / 2, A, k) → vOA'
16. Angle(Vector[B, A], Vector[O, B]) → α1
17. Rotate(vOB, α1 / 2, B, k) → vOB'
18. Ray(B, B') → g
19. Intersect(f, b1) → CenterSphere1
20. OrthogonalLine(CenterSphere1, i, k) → h
21. Intersect(i, h) → H
22. Circle(CenterSphere1, H, k) → p
23. Sphere(CenterSphere1, H) → l
24. Ray(A, A') → m
25. Intersect(f, b2) → CenterSphere2
26. OrthogonalLine(CenterSphere2, i, k) → n
27. Intersect(i, n) → M
28. Circle(CenterSphere2, M, k) → s
29. Point(EllipseHyperbola) → P
30. Line(O, P) → a_1
31. Segment(M, P) → b_1
32. Segment(P, H) → e_1
33. Sphere(CenterSphere2, M) → l'
34. OrthogonalLine(CenterSphere2, lineOA, k) → q
35. OrthogonalLine(CenterSphere1, lineOA, k) → r
36. Intersect(lineOA, r) → C
37. Intersect(q, lineOA) → D
38. Circle(f, C) → tangentCircle1
39. Circle(f, D) → tangentCircle2
40. Line(O, P) → lineOP
41. Intersect(lineOP, tangentCircle2) → TangencyP2,
42. Intersect(lineOP, tangentCircle1) → TangencyP1,
43. Segment(P, TangencyP1) → PtoTangent1
44. Segment(TangencyP2, P) → PtoTangent2
45. Segment(O, TangencyP2) → coneEdge
46. Tangent(A, EllipseHyperbola) → t,
47. Plane(t, lineOA) → tangentToConePlane
48. Plane(B, tangentToConePlane) → planeForParabola
49. IntersectPath(planeForParabola, a) → Parabola
50. Intersect(f, Parabola) → E,
51. Intersect(f, planeForParabola) → F_1
52. Line(B, F_1) → c
53. AngularBisector(f', c) → f_1, g_1
54. Intersect(g_1, f) → C_{SphereForParabola}
55. OrthogonalLine(C_{SphereForParabola}, c, space) → h_1
56. Intersect(h_1, c) → F
57. Sphere(C_{SphereForParabola}, F) → o
58. Point(Parabola) → G
59. Segment(F, G) → i_1
60. Intersect(f', o) → I, J
61. Circle(f, I) → c_1
62. Sphere(B, F) → u
63. Intersect(c, u) → K, L
64. OrthogonalPlane(K, c) → p_1
65. IntersectPath(p_1, planeForParabola) → directrix
66. OrthogonalLine(G, p_1) → k_1
67. Intersect(directrix, Parabola) → N, T
68. Intersect(directrix, k_1) → Q
69. Segment(G, O) → l_1
70. Intersect(l_1, c_1, 1) → R
71. Plane(c_1) → tangentCirclePlaneForParabola
72. OrthogonalLine(G, tangentCirclePlaneForParabola) → m_1
73. Intersect(m_1, tangentCirclePlaneForParabola) → S
74. Angle(S, G, R) → γ
75. Angle(Q, G, S) → δ
76. Segment(G, R) → j_1
77. Segment(Q, G) → n_1
78. Segment(Q, S) → q_1
79. Segment(S, R) → r_1
80. Angle(G, S, Q) → ε
81. Angle(R, S, G) → ζ
82. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → p_2
83. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → q_2
84. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → r_2
85. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → p_3
86. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → q_3
87. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → r_3
88. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → p_4
89. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → q_4
90. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → r_4
91. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → p_5
92. If(checkBoxEllHyp, checkBoxParabola + (0 * z) = false) → q_5
93. Angle(G, Q, K) → η