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将立方体剖分为 4 个相等部分

将立方体剖分为 4 个相等部分
几何画板及绘图内容加载中，请稍等……
2020-09-08 03:27
向量立体几何变换几何作图
①演示将一个立方体通过几何变换剖分为四个全等的部分。②涉及立体几何、几何变换（反射、旋转、平移）、相似变换、向量等核心概念。③作图要点：使用 Intersect、Point、Polygon、Midpoint、Segment、Circle、LineBisector、Line、Mirror、Rotate、Prism、Vector、Translate 等命令，构造顶点、棱、面、中点、镜像、旋转体等对象。④适合高中立体几何教学、几何作图训练及大学几何课程演示。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → E
  3. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  4. Midpoint(j) → L
  5. Midpoint(l) → K
  6. Segment(K, L) → p
  7. Point(p) → U
  8. Point(p) → T
  9. Midpoint(U, T) → H_1
  10. Circle(H_1, 0.95) → d_2
  11. LineBisector(T, U) → e
  12. Intersect(d_2, e, 2) → I_1
  13. Segment(H_1, I_1) → l_1
  14. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  15. Midpoint(h) → I
  16. Midpoint(f) → J
  17. Segment(I, J) → n
  18. Point(n) → M
  19. Midpoint(I, J) → N
  20. Circle(M, 0.2) → c
  21. Intersect(c, n, 2) → O
  22. Line(M, h) → q
  23. Line(O, q) → r
  24. Point(q) → P
  25. Line(P, n) → s
  26. Intersect(r, s) → Q
  27. Mirror(P, N) → P'
  28. Mirror(Q, N) → Q'
  29. Mirror(O, N) → O'
  30. Mirror(M, N) → M'
  31. Polygon(D, I, J, A, M, P, Q, O, O', Q', P', M') → poly3, d, m', j_1, a, i_1, m_1, p_1, q_1, o, o', q', p'
  32. Polygon(C, I, J, B, M, P, Q, O, O', Q', P', M') → poly4, c_1, m'_1, j_2, b, i_2, m_2, p_2, q_2, o_1, o'_1, q'_1, p'_1
  33. Midpoint(m) → R
  34. Midpoint(k) → S
  35. Segment(R, S) → t
  36. Intersect(t, p) → W
  37. Rotate(T, 90°, W) → T'
  38. Point(l_1) → V
  39. Rotate(V, 90°, W) → V'
  40. Rotate(U, 90°, W) → U'
  41. Polygon(K, H, R, T', V', U', W, U, V, T) → poly5, k_1, t_1, h_1, r_1, t', v', u', w, u_3, v
  42. Rotate(K, 90°, W) → K'
  43. Rotate(H, 90°, W) → H'
  44. Rotate(R, 90°, W) → R'
  45. Rotate(T', 90°, W) → T''
  46. Rotate(V', 90°, W) → V''
  47. Rotate(U', 90°, W) → U''
  48. Rotate(W, 90°, W) → W'
  49. Rotate(U, 90°, W) → U'_1
  50. Rotate(V, 90°, W) → V'_1
  51. Rotate(T, 90°, W) → T'_1
  52. Polygon(K', H', R', T'', V'', U'', W', U'_1, V'_1, T'_1) → poly5', k', t'_1, h', r', t'', v'', u'', w', u'_1, v'_1
  53. Rotate(K', 90°, W) → K''
  54. Rotate(H', 90°, W) → H''
  55. Rotate(R', 90°, W) → R''
  56. Rotate(T'', 90°, W) → T'''
  57. Rotate(V'', 90°, W) → V'''
  58. Rotate(U'', 90°, W) → U'''
  59. Rotate(W', 90°, W) → W''
  60. Rotate(U'_1, 90°, W) → Z
  61. Rotate(V'_1, 90°, W) → A_1
  62. Rotate(T'_1, 90°, W) → B_1
  63. Polygon(K'', H'', R'', T''', V''', U''', W'', Z, A_1, B_1) → poly5'', k'', b_1, h'', r'', t''', v''', u''', w'', z_1, a_1
  64. Rotate(K'', 90°, W) → K'''
  65. Rotate(H'', 90°, W) → H'''
  66. Rotate(R'', 90°, W) → R'''
  67. Rotate(T''', 90°, W) → C_1
  68. Rotate(V''', 90°, W) → D_1
  69. Rotate(U''', 90°, W) → E_1
  70. Rotate(W'', 90°, W) → W'''
  71. Rotate(Z, 90°, W) → Z'
  72. Rotate(A_1, 90°, W) → F_1
  73. Rotate(B_1, 90°, W) → G_1
  74. Polygon(K''', H''', R''', C_1, D_1, E_1, W''', Z', F_1, G_1) → poly5''', k''', g_1, h''', r''', c_2, d_1, e_1, w''', z', f_1
  75. Prism(poly5, n_1) → prism1, R_1, C_2, face12, face13, face15, face20, face21, face19, face18, face17, face16, S_1, face14, face22, edge22, edge21, edge23, edge28, edge29, edge30, edge27, edge25, T_1, edge26, edge24, edge31, edge33, edge34, edge35, edge36, edge37, edge38, edge39, U_1, edge40, edge32, V_1, W_1, Z_1, A_2, B_2
  76. Segment(W, K_1) → s_1
  77. Segment(W, L_1) → f_2
  78. Circle(W, (a_2 * s_1)) → e_2
  79. Intersect(s_1, e_2, 1) → M_1
  80. Intersect(f_2, e_2, 1) → N_1
  81. Vector(W, M_1) → u
  82. Vector(W, N_1) → u_1
  83. Translate(prism1, Vector[(-u_1)]) → prism1'
  84. Prism(poly5''', b_2) → prism2, K_2, T_2, face23, face25, face26, face27, face28, face29, face30, face31, face32, L_2, face24, face33, edge41, edge42, edge43, edge44, edge45, edge46, edge47, edge48, M_2, edge49, edge50, edge51, edge53, edge54, edge55, edge56, edge57, edge58, edge59, N_2, edge60, edge52, O_2, P_2, Q_2, R_2, S_2
  85. Translate(prism2, u) → prism2'
  86. Prism(poly5', g_2) → prism4, U_2, F_3, face34, face36, face37, face38, face39, face40, face41, face42, face43, V_2, face35, face44, edge61, edge62, edge63, edge64, edge65, edge66, edge67, edge68, W_2, edge69, edge70, edge71, edge73, edge74, edge75, edge76, edge77, edge78, edge79, Z_2, edge80, edge72, A_3, B_3, C_3, D_3, E_3
  87. Prism(poly5'', k_2) → prism3, G_3, P_3, face45, face47, face48, face49, face50, face51, face52, face53, face54, H_3, face46, face55, edge81, edge82, edge83, edge84, edge85, edge86, edge87, edge88, I_3, edge89, edge90, edge91, edge93, edge94, edge95, edge96, edge97, edge98, edge99, J_3, edge100, edge92, K_3, L_3, M_3, N_3, O_3
  88. Translate(prism3, u_1) → prism3'
  89. Translate(prism4, Vector[(-u)]) → prism4'

AI 绘图提示语参考

绘制一个立方体，并将其分割成四个全等的部分。首先，通过反射、旋转和平移等变换，创建立方体的顶点和边。接着，利用中点、线段和圆等工具，构造立方体的面和分割线。最后，通过镜像和旋转操作，将立方体分割成四个全等的部分。
以上提示语为根据原始绘图命令整理而来，仅供参考。