环面交线的第二轮廓点

环面交线的第二轮廓点
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2020-04-09 01:59
本范例演示了环面交线的第二轮廓点。涉及的核心数学概念包括解析几何和几何作图。通过使用GeoGebra命令如Line, Point, Circle, Intersect等,可以构造环面的交线并找到其第二轮廓点。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. Line(O', A) → f
  2. Point(f) → B
  3. Circle(O', B) → c
  4. Point(f) → C
  5. Circle(O', C) → d
  6. OrthogonalLine(O', f) → g
  7. Midpoint(B, C) → D
  8. OrthogonalLine(D, f) → h
  9. Point(g) → E
  10. OrthogonalLine(E, g) → i
  11. Intersect(h, i) → F
  12. Circle(F, Segment[D, C]) → e
  13. Mirror(e, g) → e'
  14. Mirror(h, g) → h'_1
  15. Intersect(e', h'_1, 2) → G
  16. Intersect(e, h, 2) → H
  17. Segment(G, H) → j
  18. Intersect(e', h'_1, 1) → I
  19. Intersect(e, h, 1) → J
  20. Segment(I, J) → k
  21. Line(O', K) → l
  22. OrthogonalLine(K, l) → n_1
  23. Line(I, J) → n_2
  24. Line(G, H) → p
  25. Point(l) → L
  26. OrthogonalLine(L, l) → q
  27. OrthogonalLine(K, f) → r
  28. OrthogonalLine(L, f) → s
  29. Intersect(r, n_2) → M
  30. Intersect(s, p) → N
  31. Segment(M, N) → t
  32. Point(t) → P_2
  33. OrthogonalLine(P_2, g) → a
  34. Intersect(e', a) → Q, P_0''p
  35. Intersect(e, a) → S, T
  36. Intersect(a, g) → U
  37. Circle(O', Segment[U, Q]) → c_1
  38. Circle(O', Segment[U, P_0''p]) → d_1
  39. OrthogonalLine(P_2, i) → b
  40. Intersect(l, b) → V
  41. OrthogonalLine(V, l) → f_1
  42. Center(e') → I_1
  43. Intersect(d_1, f_1) → P', Z
  44. Intersect(c_1, f_1) → A_1, B_1
  45. Locus(P', P_2) → ponthalmaz1
  46. Locus(A_1, P_2) → ponthalmaz2
  47. Locus(B_1, P_2) → ponthalmaz3
  48. Locus(Z, P_2) → ponthalmaz4
  49. OrthogonalLine(Z, f) → g_1
  50. OrthogonalLine(B_1, f) → h_1
  51. OrthogonalLine(A_1, f) → i_1
  52. OrthogonalLine(P', f) → j_1
  53. Intersect(g_1, a) → C_1
  54. Intersect(h_1, a) → D_1
  55. Segment(P_0''p, S) → k_2
  56. Intersect(i_1, a) → E_1
  57. Intersect(j_1, a) → P''
  58. Locus(P'', P_2) → ponthalmaz5
  59. Locus(E_1, P_2) → ponthalmaz6
  60. Locus(D_1, P_2) → ponthalmaz7
  61. Locus(C_1, P_2) → ponthalmaz8
  62. Point(n_1) → O
  63. OrthogonalLine(O, n_1) → m
  64. Intersect(q, m) → P
  65. Mirror(m, O') → m'
  66. Intersect(n_1, m') → R
  67. Intersect(q, m') → W
  68. OrthogonalLine(O, n_2) → n
  69. OrthogonalLine(P, n_2) → k_1
  70. OrthogonalLine(R, n_2) → l_1
  71. OrthogonalLine(W, p) → m_1
  72. Intersect(n, n_2) → F_1
  73. Intersect(k_1, p) → G_1
  74. Intersect(l_1, n_2) → H_1
  75. Intersect(m_1, p) → J_1
  76. Polygon(P, W, R, O) → q1, h', w, r_1, o
  77. Polygon(F_1, G_1, J_1, H_1) → q2, s_1, h'', a_1, b_1
  78. OrthogonalLine(O', l_1) → e_1
  79. Intersect(e_1, q) → K_1
  80. Intersect(e_1, n_1) → L_1
  81. Segment(L_1, K_1) → v'
  82. OrthogonalLine(L_1, n_2) → g_2
  83. OrthogonalLine(K_1, n_2) → h_2
  84. Intersect(g_2, n_2) → M_1
  85. Intersect(h_2, p) → N_1
  86. Line(O', P') → q_1
  87. Segment(L_1, M_1) → i_2
  88. Segment(K_1, N_1) → j_2
  89. Segment(M_1, N_1) → v''
  90. Intersect(e', v'') → O_1, P_1
  91. Intersect(e, v'') → Q_1, R_1
  92. OrthogonalLine(O_1, p) → m_2
  93. OrthogonalLine(P_1, p) → p_2
  94. OrthogonalLine(Q_1, n_2) → q_2
  95. OrthogonalLine(R_1, n_2) → r_2
  96. Intersect(r_2, e_1) → S_1
  97. Intersect(q_2, e_1) → T_1
  98. Intersect(p_2, e_1) → U_1
  99. Intersect(m_2, e_1) → V_1
  100. Segment(O_1, V_1) → s_2
  101. Segment(U_1, P_1) → t_2
  102. Segment(Q_1, T_1) → a_2
  103. Segment(S_1, R_1) → b_2

AI 绘图提示语参考

绘制一个环面的第二轮廓点。首先,创建一个通过点O'和A的直线f,然后在f上取点B和C,分别以O'为圆心,B和C为半径画圆c和d。接着,构造与f正交的直线g,并找到B和C的中点D,再以D为圆心,f为轴构造直线h。通过一系列交点和镜像操作,最终得到环面的第二轮廓点P2。
以上提示语为根据原始绘图命令整理而来,仅供参考。