探索等距平面

探索等距平面
几何画板及绘图内容加载中,请稍等……
2013-10-14 02:41
①本范例演示在三维等距网格上观察xy、xz和yz平面的外观;②涉及的核心数学概念包括平面、向量、多边形和立体几何;③作图要点——使用了Line(线)、Point(点)、Intersect(交点)、Polygon(多边形)等GeoGebra命令;④适合高中阶段学习立体几何的学生使用。

GeoGebra 命令及参数

  1. Line(O, z_1) → a
  2. Line(O, x_1) → b
  3. Line(O, y_1) → c
  4. Line(z_1, b) → d
  5. Line(z_2, d) → e
  6. Line(z_3, e) → f
  7. Line(z_4, f) → g
  8. Line(z_5, g) → h
  9. Line(z_6, h) → i
  10. Line(y_{-7}, i) → j
  11. Line(y_{-8}, j) → k
  12. Line(y_{-9}, k) → l
  13. Line(y_{-10}, l) → m
  14. Line(y_{-11}, m) → n
  15. Line(y_{-12}, n) → p
  16. Line(y_{-13}, p) → q
  17. Point(c) → A
  18. Line(A, q) → r
  19. Line(y_1, d) → s
  20. Line(y_2, s) → t
  21. Line(y_3, t) → a_1
  22. Line(y_4, a_1) → b_1
  23. Line(y_5, b_1) → c_1
  24. Line(y_6, c_1) → d_1
  25. Line(y_7, d_1) → e_1
  26. Line(y_8, e_1) → f_1
  27. Line(y_9, f_1) → g_1
  28. Line(y_{10}, g_1) → h_1
  29. Line(y_{11}, h_1) → i_1
  30. Line(y_{12}, i_1) → j_1
  31. Line(B, j_1) → k_1
  32. Line(C, k_1) → l_1
  33. Line(x_1, a) → m_1
  34. Line(x_2, m_1) → n_1
  35. Line(x_3, n_1) → p_1
  36. Line(x_4, p_1) → q_1
  37. Line(x_5, q_1) → r_1
  38. Line(x_6, r_1) → s_1
  39. Line(x_7, s_1) → t_1
  40. Line(x_8, t_1) → a_2
  41. Line(x_9, a_2) → b_2
  42. Line(x_{10}, b_2) → c_2
  43. Line(x_{11}, c_2) → d_2
  44. Line(x_{12}, d_2) → e_2
  45. Point(b) → D
  46. Line(D, e_2) → f_2
  47. Point(b) → E
  48. Line(E, f_2) → g_2
  49. Line(F, g_2) → h_2
  50. Line(G, h_2) → i_2
  51. Line(H, i_2) → j_2
  52. Line(x_{-1}, a) → k_2
  53. Line(x_{-2}, k_2) → l_2
  54. Line(x_{-3}, l_2) → m_2
  55. Line(x_{-4}, m_2) → n_2
  56. Line(x_{-5}, n_2) → p_2
  57. Line(x_{-6}, p_2) → q_2
  58. Line(x_{-7}, q_2) → r_2
  59. Line(x_{-8}, r_2) → s_2
  60. Line(x_{-9}, s_2) → t_2
  61. Line(x_{-10}, t_2) → a_3
  62. Line(x_{-11}, a_3) → b_3
  63. Line(x_{-12}, b_3) → c_3
  64. Line(I, c_3) → d_3
  65. Line(J, d_3) → e_3
  66. Line(K, e_3) → f_3
  67. Line(x_{-1}, c) → g_3
  68. Line(x_{-2}, g_3) → h_3
  69. Line(x_{-3}, h_3) → i_3
  70. Line(x_{-4}, i_3) → j_3
  71. Line(x_{-5}, j_3) → k_3
  72. Line(x_{-6}, k_3) → l_3
  73. Line(x_{-7}, l_3) → m_3
  74. Line(x_{-8}, m_3) → n_3
  75. Line(x_{-9}, n_3) → p_3
  76. Line(x_{-10}, p_3) → q_3
  77. Line(x_{-11}, q_3) → r_3
  78. Line(x_{-12}, r_3) → s_3
  79. Line(L, s_3) → t_3
  80. Line(x_1, c) → a_4
  81. Line(x_2, a_4) → b_4
  82. Line(x_3, b_4) → c_4
  83. Line(x_4, c_4) → d_4
  84. Line(x_5, d_4) → e_4
  85. Line(x_6, e_4) → f_4
  86. Line(x_7, f_4) → g_4
  87. Line(x_8, g_4) → h_4
  88. Line(x_9, h_4) → i_4
  89. Line(x_{10}, i_4) → j_4
  90. Line(x_{11}, j_4) → k_4
  91. Line(x_{12}, k_4) → l_4
  92. Intersect(b, f_2) → M
  93. Line(M, l_4) → m_4
  94. Intersect(b, g_2) → N
  95. Line(N, m_4) → n_4
  96. Line(P, n_4) → p_4
  97. Polygon(Q, R, S, T) → poly1, q_4, r_4, s_4, t_4

AI 绘图提示语参考

在一个三维等距网格中,绘制三个互相垂直的平面,分别代表xy、xz和yz平面。首先画出网格的基线,然后通过这些基线构建出三个平面的轮廓,每个平面由多个线段和顶点组成。先绘制xy平面,再绘制xz平面,最后绘制yz平面,注意每个平面的顶点与网格基线的交点关系,确保三个平面在空间中正确相交。
以上提示语为根据原始绘图命令整理而来,仅供参考。