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四维空间中平面内圆的构造

四维空间中平面内圆的构造
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2019-08-29 18:39
圆解析几何几何作图
所属专题 Spherical sections of a 3-Sphere
本范例展示了如何在四维空间中构造一个平面内的圆。核心数学概念包括四维空间中的几何构造和解析几何。通过使用GeoGebra命令如Point, Intersect, Vector, Line等，可以精确地构建出所需的圆。适合高中及以上学生或教师用于教学和学习四维空间几何。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(zAxis) → C
  3. Point(zAxis) → D
  4. Intersect(xAxis, zAxis) → O
  5. Vector(O, A) → xdir
  6. Point(yAxis) → B
  7. Vector(O, B) → ydir
  8. Vector(O, D) → wdir
  9. Vector(O, C) → zdir
  10. Line(O, D) → f
  11. Line(O, A) → g
  12. Line(O, B) → h
  13. PointIn(p) → E
  14. PointIn(p) → F
  15. Line(E, F) → z_4
  16. Line(I, J) → w_3
  17. Plane(G, z_4) → α_4
  18. Plane(H, w_3) → α_3
  19. OrthogonalLine(I, xOyPlane) → k
  20. Intersect(k, α_4) → K
  21. OrthogonalLine(J, xOyPlane) → l
  22. Intersect(l, α_4) → L
  23. Line(L, K) → w_4
  24. OrthogonalLine(F, xOyPlane) → n
  25. OrthogonalLine(E, xOyPlane) → s
  26. Intersect(s, α_3) → M
  27. Intersect(n, α_3) → N
  28. Line(M, N) → z_3
  29. PointIn(α_3) → S_3
  30. OrthogonalLine(S_3, xOyPlane) → b
  31. Intersect(b, α_4) → S_4
  32. Segment(S_3, S_4) → f_2
  33. OrthogonalLine(S_3, α_3) → a
  34. Intersect(b, xOyPlane) → S_0
  35. Distance(S_0, S_4) → w
  36. Sphere(S_3, w) → c
  37. Intersect(a, c) → S_r, Q
  38. Plane(S_r, z_3) → p_1
  39. Circle(S_r, rho, p_1) → d
  40. OrthogonalPlane(S_r, z_3) → q_1
  41. IntersectPath(q_1, α_3) → e
  42. IntersectPath(p_1, q_1) → f_1
  43. Intersect(f_1, d) → P, R
  44. OrthogonalLine(S_r, q_1) → g_1
  45. Intersect(g_1, d) → S, T
  46. Line(P, a) → h_1
  47. Line(T, a) → i_1
  48. Line(S, a) → j_1
  49. Line(R, a) → k_1
  50. Intersect(h_1, α_3) → U
  51. Intersect(k_1, α_3) → V
  52. Intersect(i_1, α_3) → W
  53. Intersect(j_1, α_3) → Z
  54. Line(W, Z) → l_1
  55. Segment(P, U) → l_2
  56. Segment(R, V) → k_2
  57. Segment(W, T) → m_2
  58. Segment(Z, S) → n_2
  59. Circle(U, rho, α_3) → c_1
  60. Intersect(p_1, c_1) → A_1,
  61. Intersect(l_1, c_1) → B_1, C_1
  62. Line(U, f) → m_1
  63. Line(V, f) → n_1
  64. Line(W, f) → r_1
  65. Line(Z, f) → s_1
  66. Ellipse(B_1, C_1, U) → d_1
  67. Intersect(n_1, α_4) → D_1
  68. Intersect(s_1, α_4) → E_1
  69. Intersect(r_1, α_4) → F_1
  70. Intersect(m_1, α_4) → G_1
  71. Segment(V, D_1) → h_2
  72. Segment(F_1, W) → i_2
  73. Segment(G_1, U) → g_2
  74. Segment(E_1, Z) → j_2
  75. Line(F_1, E_1) → t_1
  76. Line(G_1, D_1) → a_1
  77. OrthogonalLine(G_1, α_4) → b_1
  78. Circle(G_1, rho, b_1) → e_1
  79. Intersect(t_1, e_1) → H_1, I_1
  80. Ellipse(I_1, H_1, G_1) → c_2
  81. Circle(a, Z) → d_2
  82. Distance(S_3, U) → a_3
  83. Distance(S_4, G_1) → a_4
  84. Circle(S_4, rho, α_4) → e_2