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球体与多边形交点演示

球体与多边形交点演示
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2017-08-19 14:44
向量解析几何立体几何微积分几何作图
①本范例演示球体与多边形（如三角形）的交点计算与可视化；②涉及核心数学概念包括立体几何、解析几何、向量运算、导数计算；③构造要点：使用Textfield、Segment、Rotate、CircleArc、Distance、Intersect、Point、Mirror、Line、Vector、Translate等GeoGebra命令创建几何对象并计算交点；④适合高中及以上学生及数学爱好者用于理解空间几何与微积分应用。

GeoGebra 命令及参数

  1. Textfield(a) → InputBox1
  2. Segment(A, B) → f
  3. Rotate(A, 32°, A) → A'
  4. Rotate(B, 32°, A) → B'
  5. CircleArc(C, H, I) → h
  6. Segment(H, I) → g_Π
  7. Distance(K, L) → distanceKL
  8. Distance(M, N) → distanceMN
  9. Segment(N, M) → i
  10. Segment(L, K) → j
  11. Segment(K, N) → k_Φ
  12. Segment(M, L) → l
  13. Intersect(i, j) → O
  14. Segment(F, G_2) → m
  15. Segment(D, E) → p
  16. Point(j) → R
  17. Segment(M, R) → q
  18. Mirror(M, j) → M'
  19. Mirror(R, j) → R'
  20. Mirror(M, i) → M'_1
  21. Mirror(R, i) → R'_1
  22. Segment(M'_1, R'_1) → q'_1
  23. Segment(R', N) → s
  24. Segment(N, R'_1) → t
  25. Point(j) → S
  26. Segment(R'_1, S) → r
  27. Point(r) → T
  28. Segment(R, T) → a_1
  29. Distance(T, R'_1) → distanceTR'1
  30. Line(R'_1, t) → b_1
  31. Line(T, a_1) → c_1
  32. Segment(R'_1, T) → d_1
  33. Intersect(i, q) → U
  34. Segment(T, U) → e_1
  35. Segment(C, B) → f_1
  36. Segment(C, A) → g_1
  37. Segment(R', U) → h_1
  38. Intersect(i, j) → V
  39. Line(V, h_1) → i_1
  40. Mirror(R', i_1) → R''
  41. Mirror(U, i_1) → U'
  42. Segment(R'', U') → j_1
  43. Line(V, s) → k_1
  44. Mirror(R', k_1) → R''_1
  45. Mirror(N, k_1) → N'
  46. Segment(R''_1, N') → s'
  47. Vector(W, Z) → u
  48. Translate(R''_1, u) → A_1
  49. Translate(N', u) → N''
  50. Segment(A_1, N'') → s''
  51. Mirror(A_1, k_1) → B_1
  52. Mirror(N'', k_1) → N'''
  53. Segment(B_1, N''') → s'''
  54. Vector(C_1, D_1) → v
  55. Translate(B_1, v) → E_1
  56. Translate(N''', v) → F_1
  57. Vector(G_1, H_1) → w
  58. Translate(R'', w) → R'''
  59. Translate(U', w) → U''
  60. Segment(R''', U'') → l_1
  61. Point(j) → K_1
  62. Point(p) → L_1
  63. Segment(K_1, L_1) → m_1
  64. Point(p) → N_1
  65. Point(j) → O_1
  66. Segment(N_1, O_1) → q_1
  67. Point(i) → P_1
  68. Point(j) → Q_1
  69. Segment(P_1, Q_1) → r_1
  70. Point(f) → M_1
  71. Segment(M_1, R_1) → n_1
  72. Segment(M_1, S_1) → p_1
  73. Point(p) → T_1
  74. Segment(S_1, T_1) → s_1
  75. Segment(S_1, U_1) → t_1
  76. Segment(U_1, R_1) → a_2
  77. Segment(N_1, U_1) → b_2
  78. Segment(V_1, W_1) → c_2
  79. Segment(Z_1, A_2) → d_2
  80. Segment(N, B) → f_2
  81. Segment(B, A) → g_2
  82. Segment(N, A) → h_2
  83. Segment(Q, B_2) → i_2
  84. Segment(C_2, D_2) → j_2
  85. Segment(E_2, F_2) → k_2