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用圆和直线构造椭球体

用圆和直线构造椭球体
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2019-07-29 03:39
圆解析几何立体几何
这个范例展示了如何使用圆和直线构造椭球体。它涉及圆、直线和线性方程的核心数学概念。通过使用GeoGebra命令如Circle、Intersect、Point等，可以构建出椭球体的几何模型。适合高中数学教学和学习，特别是解析几何和立体几何的内容。

GeoGebra 命令及参数

  1. Circle(O, 30, zAxis) → c
  2. Circle(O, 30, yAxis) → d
  3. Circle(O, 30, xAxis) → e
  4. AngularBisector(D, O, B) → s
  5. AngularBisector(C, O, B) → t
  6. AngularBisector(A, O, E) → a
  7. AngularBisector(E, O, B) → b
  8. AngularBisector(D, O, F) → f_1
  9. AngularBisector(D, O, E) → g_1
  10. Circle(O, 20, zAxis) → c_1
  11. Circle(O, 20, xAxis) → d_1
  12. Circle(O, 20, yAxis) → e_1
  13. Intersect(yAxis, c_1, 1) → G
  14. Intersect(yAxis, d_1, 2) → H
  15. Intersect(c_1, e_1, 1) → J
  16. Intersect(zAxis, e_1, 1) → K
  17. Intersect(zAxis, d_1, 2) → L
  18. Circle(K, 20, zAxis) → h_1
  19. Circle(L, 20, zAxis) → k_1
  20. Circle(J, 20, xAxis) → p_1
  21. Circle(H, 20, yAxis) → r_1
  22. Circle(G, 20, yAxis) → s_1
  23. Point(c) → M
  24. Intersect(s, c, 2) → N
  25. Intersect(t, c, 1) → P
  26. Intersect(t, c, 2) → Q
  27. Segment(D, B) → i_1
  28. Segment(B, C) → j_1
  29. Segment(C, A) → l_1
  30. Segment(A, D) → m_1
  31. Segment(Q, M) → n_1
  32. Segment(M, P) → t_1
  33. Segment(P, N) → a_1
  34. Segment(N, Q) → b_1
  35. Segment(Q, B) → f_2
  36. Segment(Q, C) → g_2
  37. Segment(A, M) → h_2
  38. Segment(A, P) → i_2
  39. Segment(M, C) → j_2
  40. Segment(B, N) → k_2
  41. Segment(D, P) → l_2
  42. Segment(D, N) → m_2
  43. Intersect(g_1, e, 1) → R
  44. Intersect(g_1, e, 2) → S
  45. Intersect(f_1, e, 2) → T
  46. Intersect(f_1, e, 1) → U
  47. Segment(R, T) → n_2
  48. Segment(T, S) → p_2
  49. Segment(S, U) → q_2
  50. Segment(U, R) → r_2
  51. Segment(D, E) → s_2
  52. Segment(E, C) → t_2
  53. Segment(C, F) → a_2
  54. Segment(F, D) → b_2
  55. Segment(U, E) → c_2
  56. Segment(U, C) → d_2
  57. Segment(T, D) → e_2
  58. Segment(T, F) → f_3
  59. Segment(S, D) → g_3
  60. Segment(S, E) → h_3
  61. Segment(R, F) → i_3
  62. Segment(R, C) → j_3
  63. Intersect(b, d, 1) → V
  64. Intersect(a, d, 1) → W
  65. Intersect(b, d, 2) → Z
  66. Intersect(a, d, 2) → A_1
  67. Segment(A_1, V) → k_3
  68. Segment(V, W) → l_3
  69. Segment(W, Z) → m_3
  70. Segment(Z, A_1) → n_3
  71. Segment(B, E) → p_3
  72. Segment(E, A) → q_3
  73. Segment(A, F) → r_3
  74. Segment(F, B) → s_3
  75. Segment(B, W) → t_3
  76. Segment(B, Z) → a_3
  77. Segment(V, F) → b_3
  78. Segment(F, W) → c_3
  79. Segment(V, A) → d_3
  80. Segment(E, A_1) → e_3
  81. Segment(E, Z) → f_4
  82. Segment(A_1, A) → g_4
  83. Intersect(c_1, e_1, 2) → I
  84. Circle(I, 20, xAxis) → q_1
  85. Line(B, A) → h_4
  86. Line(D, C) → i_4
  87. Line(E, F) → j_4
  88. Circle(P, V, M) → c_4
  89. Circle(W, Q, Z) → d_4
  90. Circle(V, R, W) → e_4
  91. Circle(M, R, Q) → k_4
  92. Circle(Z, U, A_1) → p_4
  93. Circle(N, S, P) → q_4