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球体与三个圆锥的接触

球体与三个圆锥的接触
几何画板及绘图内容加载中，请稍等……
2017-04-10 18:11
圆立体几何几何作图
所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
①本范例演示球体与三个圆锥相切形成的几何关系；②涉及核心数学概念包括球体、圆锥、切线、中点、垂线、交点等；③作图要点提炼自构造摘要，使用了Circle（圆）、Line（直线）、Intersect（交点）、Midpoint（中点）、OrthogonalLine（垂线）、Point（点）、Segment（线段）、Center（中心）、Cone（圆锥）、Sphere（球体）等命令和对象；④适合高中立体几何教学和几何作图练习。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Circle(B, A) → d
  3. Line(A, B) → f
  4. Intersect(d, f, 2) → D
  5. Circle(D, B) → e
  6. Circle(D, A) → g
  7. Circle(A, D) → h
  8. Intersect(g, h, 1) → C
  9. Midpoint(C, A) → E
  10. Circle(C, E) → k
  11. OrthogonalLine(A, xAxis) → i
  12. OrthogonalLine(D, xAxis) → j
  13. OrthogonalLine(C, xAxis) → l
  14. Intersect(e, k, 1) → F
  15. Point(i) → G
  16. OrthogonalLine(G, i) → m
  17. Intersect(l, m) → H
  18. Intersect(j, m) → I
  19. Intersect(i, xAxis) → J
  20. Intersect(l, xAxis) → K
  21. Intersect(j, xAxis) → L
  22. Circle(J, Segment[B, A]) → p
  23. Circle(K, Segment[B, A]) → q
  24. Circle(L, Segment[B, A]) → r_2
  25. Intersect(r_2, xAxis, 2) → M
  26. Intersect(q, xAxis, 2) → N
  27. Intersect(p, xAxis, 1) → O
  28. Intersect(q, xAxis, 1) → P
  29. Intersect(p, xAxis, 2) → Q
  30. Intersect(r_2, xAxis) → R, S
  31. Segment(O, G) → n
  32. Segment(G, Q) → s
  33. Segment(P, H) → t
  34. Segment(H, N) → a
  35. Segment(R, I) → b
  36. Segment(I, M) → f_1
  37. Segment(G, A) → g_1
  38. Segment(H, C) → h_1
  39. Segment(I, D) → i_1
  40. OrthogonalLine(M, xAxis) → j_1
  41. OrthogonalLine(R, xAxis) → k_1
  42. Intersect(e, k_1, 1) → T
  43. Intersect(e, j_1, 1) → U
  44. Segment(M, U) → l_1
  45. Segment(R, T) → m_1
  46. OrthogonalLine(N, xAxis) → n_1
  47. OrthogonalLine(P, xAxis) → p_1
  48. Intersect(k, p_1, 1) → V
  49. Intersect(k, n_1, 1) → W
  50. Segment(N, W) → q_1
  51. Segment(P, V) → r_1
  52. OrthogonalLine(O, xAxis) → s_1
  53. OrthogonalLine(Q, xAxis) → t_1
  54. Intersect(c, s_1, 1) → Z
  55. Intersect(c, t_1, 1) → A_1
  56. Segment(O, Z) → a_1
  57. Segment(Q, A_1) → b_1
  58. Circle(A, C, D) → c_1
  59. Center(c_1) → B_1
  60. Segment(F_1, C_1) → d_1
  61. Circle(d_1, G_1) → e_1
  62. Segment(A, B) → f_2
  63. Cone(C_1, F_1, f_2) → o, c_2, u
  64. Segment(H_1, E_1) → g_2
  65. Cone(E_1, H_1, f_2) → v, d_2, w
  66. Segment(I_1, D_1) → h_2
  67. Cone(D_1, I_1, f_2) → o_1, e_2, u_1
  68. OrthogonalLine(J_1, xOyPlane) → i_2
  69. Segment(B_1, D) → j_2
  70. Line(D, xAxis) → k_2
  71. Circle(D, B_1) → p_2
  72. Intersect(p_2, k_2, 2) → K_1
  73. OrthogonalLine(K_1, k_2) → l_2
  74. Intersect(l_2, xAxis) → L_1
  75. OrthogonalLine(M, f_1) → m_2
  76. Circle(M, r) → q_2
  77. Intersect(q_2, m_2, 2) → M_1
  78. OrthogonalLine(M_1, m_2) → n_2
  79. Intersect(l_2, n_2) → N_1
  80. Sphere(O_1, r) → v_1

AI 绘图提示语参考

画一个球体与三个圆锥相切，展示它们的几何关系。先画出两个相切的圆，再找到它们的交点，以此为基础构造其他圆和线段。接着，找到圆与线的交点，确定球体的接触点。绘制垂直于x轴的线，找到关键点并连接它们，形成球体与圆锥的切线。最后，用线段连接各点，完成球体与三个圆锥相切的几何图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。