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三维球面两点截面

三维球面两点截面
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2019-08-30 17:36
向量立体几何参数方程几何作图
所属专题 Spherical sections of a 3-Sphere
①本范例演示三维球面在两点处的截面图形；②涉及核心数学概念包括立体几何、向量运算、参数方程及空间几何关系；③构造过程中运用了点、线、球面、向量、正交线、平面、轨迹等 GeoGebra 命令与对象；④适合高中及以上学生及空间几何爱好者学习使用。

GeoGebra 命令及参数

  1. Point(zAxis) → S_4
  2. Intersect(zAxis, yAxis) → O
  3. Sphere(S_4, 1) → Σ_4
  4. Point(zAxis) → S_3
  5. Sphere(S_3, 1) → Σ_3
  6. Point(xAxis) → D
  7. Line(O, D) → f
  8. Point(yAxis) → E
  9. Line(O, E) → g
  10. Line(O, S_4) → h
  11. Vector(O, D) → xdir
  12. Vector(O, E) → ydir
  13. Vector(O, S_4) → wdir
  14. Vector(O, S_3) → zdir
  15. OrthogonalLine(B_1, xOyPlane) → i
  16. OrthogonalLine(A_1, xOyPlane) → j
  17. Point(j) → A_4
  18. Point(i) → B_4
  19. Point(j) → A_3
  20. Point(i) → B_3
  21. Line(A_4, B_4) → p_4
  22. Line(A_3, B_3) → p_3
  23. Segment(A_3, A_4) → k_1
  24. Segment(B_3, B_4) → l_1
  25. Intersect(p_4, xOyPlane) → Z_4
  26. Intersect(p_3, xOyPlane) → W_3
  27. OrthogonalLine(W_3, xOyPlane) → m
  28. OrthogonalLine(Z_4, xOyPlane) → n
  29. Intersect(n, p_3) → Z_3
  30. Intersect(p_4, m) → W_4
  31. Segment(Z_3, Z_4) → k
  32. Segment(W_4, W_3) → l
  33. Plane(p_3, p_4) → ρ
  34. IntersectPath(ρ, Σ_3) → σ_3
  35. Center(σ_3) → C_3
  36. OrthogonalLine(C_3, ρ) → r_1
  37. Distance(S_4, O) → r
  38. Sphere(C_3, r) → a
  39. Intersect(r_1, a) → C_r, C
  40. Segment(C_3, C_r) → m_1
  41. Radius(σ_3) → q
  42. Sphere(C_r, q) → σ_r
  43. OrthogonalLine(W_3, ρ) → s
  44. Distance(W_3, W_4) → w
  45. Sphere(W_3, w) → d
  46. Intersect(s, d) → A, W_r
  47. Segment(W_r, W_3) → c
  48. Line(W_r, Z_3) → p_r
  49. Intersect(p_r, σ_r) → V_r, U_r
  50. OrthogonalLine(V_r, ρ) → e
  51. OrthogonalLine(U_r, ρ) → f_1
  52. Intersect(f_1, p_3) → U_3
  53. Intersect(e, p_3) → V_3
  54. Segment(U_3, V_3) → j_1
  55. OrthogonalLine(V_3, xOyPlane) → g_1
  56. OrthogonalLine(U_3, xOyPlane) → h_1
  57. Intersect(h_1, p_4) → U_4
  58. Intersect(g_1, p_4) → V_4
  59. Segment(V_3, V_4) → t
  60. Segment(U_4, U_3) → b
  61. Segment(U_4, V_4) → i_1