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Explore the Isometric Planes

Explore the Isometric Planes
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2013-10-14 02:41
VectorSolid GeometryGeometric Construction
This example demonstrates observing the appearance of the xy, xz, and yz planes on a 3-d isometric grid. It involves core math concepts like planes, vectors, polygons, and solid geometry. Constructed using GeoGebra commands such as Line, Point, Intersect, and Polygon. Suitable for high school students learning solid geometry.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw three mutually perpendicular planes in a 3D isometric grid representing the xy, xz, and yz planes. Start by sketching the grid's base lines, then use these lines to construct the outlines of the three planes, each formed by multiple segments and vertices. Begin with the xy plane, then the xz plane, and finally the yz plane, ensuring the vertices of each plane intersect the grid lines correctly to maintain proper spatial orientation.
The prompt above was compiled from the original drawing commands and is for reference only.