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立方体分割为7部分

立方体分割为7部分
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2018-12-26 03:15
立体几何几何作图
这个范例演示如何将一个立方体分割为7个相等的部分。涉及的核心数学概念包括立方体的分割、体积和表面积的计算。通过使用GeoGebra命令如Intersect、Point、Cube等，可以构造出立方体的各个面和边。适合初中或高中学生学习立体几何和分割问题。

GeoGebra 命令及参数

  1. Intersect(xAxis, zAxis) → A
  2. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  3. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeBD, edgeAB, edgeAC, edgeCD, edgeBE, edgeDH, edgeEH, edgeEF, E, edgeAF, edgeFG, edgeCG, edgeGH, F, G, H, faceABDC, faceBDHE, faceABEF, faceACGF
  4. Midpoint(H, B) → C_p
  5. Line(C_p, zAxis) → f
  6. Sphere(C_p, (0.25 * 7^(2 / 3))) → b
  7. Line(C_p, xAxis) → g
  8. Line(C_p, yAxis) → h
  9. Intersect(f, b) → J, K
  10. Intersect(g, b) → L, M
  11. Intersect(h, b) → N, O
  12. Plane(L, faceBDHE) → c
  13. Plane(M, faceACGF) → d_1
  14. Plane(K, faceEFGH) → e
  15. IntersectPath(c, e) → i
  16. IntersectPath(d_1, e) → j
  17. Plane(J, e) → k
  18. Plane(N, faceABEF) → l
  19. Plane(O, faceCDHG) → m
  20. IntersectPath(d_1, l) → n
  21. IntersectPath(d_1, m) → p
  22. Intersect(j, n) → F'
  23. Intersect(j, p) → G'_2
  24. IntersectPath(c, m) → q
  25. IntersectPath(c, l) → r
  26. IntersectPath(d_1, k) → s
  27. IntersectPath(c, k) → t
  28. Intersect(s, n) → B'
  29. Intersect(p, s) → C'
  30. Intersect(t, q) → D'
  31. Intersect(r, t) → A'
  32. Intersect(i, r) → E'_2
  33. Cube(A', B', C') → o, D'_2, faceC'RWU, faceSTUW, edgeA'R, edgeA'B', edgeB'C', edgeC'R, edgeA'S, edgeRW, edgeSW, edgeST, E', edgeB'T, edgeTU, edgeC'U, edgeUW, F'_2, G', H', faceA'B'C'R, faceA'RWS, faceA'B'TS, faceB'C'UT
  34. Sphere(C_p, d) → v
  35. Sphere(C_p, d) → u
  36. Intersect(h, u) → I, P
  37. Intersect(f, u) → Q, R
  38. Intersect(g, u) → S, T
  39. Vector(N, I) → y_2
  40. Vector(O, P) → y_1
  41. Vector(M, T) → x_1
  42. Vector(L, S) → x_2
  43. Vector(K, R) → z_1
  44. Vector(J, Q) → z_2
  45. Polygon(G, H, D, C) → q1_{y1}, g_1, h_1, d_2, c_1
  46. Polygon(G, G', C', C) → t2_{y1}, g_2, g', c', c_2
  47. Polygon(H, H', G', G) → t1_{y1}, h_2, h', g'_1, g_3
  48. Polygon(D, D', H', H) → t4_{y1}, d_3, d', h'_1, h_3
  49. Polygon(D, C, C', D') → t3_{y1}, d_4, c_3, c'_1, d'_1
  50. Translate(q1_{y1}, y_1) → q1'_{y1}
  51. Translate(t1_{y1}, y_1) → t1'_{y1}
  52. Translate(t2_{y1}, y_1) → t2'_{y1}
  53. Translate(t3_{y1}, y_1) → t3'_{y1}
  54. Translate(t4_{y1}, y_1) → t4'_{y1}
  55. Translate(faceC'RWU, y_1) → faceC'RWU'
  56. OrthogonalLine(H', g_1, space) → f_1
  57. Intersect(g_1, f_1) → U
  58. Segment(U, H') → i_1
  59. Midpoint(V, W) → Z
  60. Segment(V, W) → j_1
  61. OrthogonalLine(Z, j_1) → k_1
  62. Circle(Z, Distance[H', U]) → e_1
  63. Intersect(e_1, k_1, 2) → A_1
  64. Line(A_1, j_1) → l_1
  65. Circle(A_1, Distance[G', H'] / 2) → p_1
  66. Intersect(p_1, l_1) → B_1, C_1
  67. Segment(V, B_1) → m_1
  68. Segment(C_1, W) → n_1
  69. Polygon(B_1, V, W, C_1) → flat_{trap1}, b_1, v_1, w, c_4
  70. Polygon(B_1, C_1, 4) → poly1, q_1, r_1, s_1, t_1, D_1, E_1
  71. Polygon(W, V, 4) → poly2, a_1, f_2, i_2, j_2, F_1, G_1
  72. Midpoint(F_1, W) → H_1
  73. Rotate(B_1, 90°, H_1) → I_1
  74. Rotate(V, 90°, H_1) → V'
  75. Rotate(W, 90°, H_1) → W'
  76. Rotate(C_1, 90°, H_1) → J_1
  77. Polygon(I_1, V', W', J_1) → flat_{trap4}, i_3, v', w', j_3
  78. Rotate(I_1, 90°, H_1) → K_1
  79. Rotate(V', 90°, H_1) → V''
  80. Rotate(W', 90°, H_1) → W''
  81. Rotate(J_1, 90°, H_1) → L_1
  82. Polygon(K_1, V'', W'', L_1) → flat_{trap3}, k_2, v'', w'', l_2
  83. Rotate(K_1, 90°, H_1) → M_1
  84. Rotate(V'', 90°, H_1) → V'''
  85. Rotate(W'', 90°, H_1) → W'''
  86. Rotate(L_1, 90°, H_1) → N_1
  87. Polygon(M_1, V''', W''', N_1) → flat_{trap2}, m_2, v''', w''', n_2
  88. Rotate(faceC'RWU', 90°, f) → faceC'RWU'_{90}
  89. Rotate(faceC'RWU'_{90}, 90°, f) → faceC'RWU'_{180}
  90. Rotate(q1'_{y1}, 90°, f) → q1'_{y1}90
  91. Rotate(q1'_{y1}90, 90°, f) → q1'_{y1}180
  92. Rotate(t1'_{y1}, 90°, f) → t1'_{y1}90
  93. Rotate(t2'_{y1}, 90°, f) → t2'_{y1}90
  94. Rotate(t3'_{y1}, 90°, f) → t3'_{y1}90
  95. Rotate(t4'_{y1}, 90°, f) → t4'_{y1}90
  96. Rotate(t2'_{y1}, 180°, f) → t2'_{y1}180
  97. Rotate(t1'_{y1}, 180°, f) → t1'_{y1}180
  98. Rotate(t3'_{y1}, 180°, f) → q5
  99. Rotate(t4'_{y1}, 180°, f) → q6
  100. Rotate(t1'_{y1}90, 180°, f) → t1'_{y1}270
  101. Rotate(t2'_{y1}90, 180°, f) → t2'_{y1}270
  102. Rotate(q1'_{y1}90, 180°, f) → q1'_{y1}270
  103. Rotate(t3'_{y1}90, 180°, f) → t3'_{y1}270
  104. Rotate(t4'_{y1}90, 180°, f) → t4'_{y1}270
  105. Rotate(faceC'RWU'_{90}, 180°, f) → faceC'RWU'_{270}
  106. Rotate(faceC'RWU', (-(90°)), g) → faceC'RWU'_{bottom}
  107. Rotate(q1'_{y1}, (-(90°)), g) → q1'_{y1}bottom
  108. Rotate(t1'_{y1}, (-(90°)), g) → t1'_{y1}bottom
  109. Rotate(t2'_{y1}, (-(90°)), g) → t2'_{y1}bottom
  110. Rotate(t3'_{y1}, (-(90°)), g) → t3'_{y1}bottom
  111. Rotate(t4'_{y1}, (-(90°)), g) → t4'_{y1}bottom
  112. Rotate(q1'_{y1}bottom, (-(180°)), g) → q1'_{y1}top
  113. Rotate(faceC'RWU'_{bottom}, 180°, g) → faceC'RWU'_{top}
  114. Rotate(t1'_{y1}bottom, 180°, g) → t1'_1
  115. Rotate(t2'_{y1}bottom, 180°, g) → t2'_{y1}top
  116. Rotate(t3'_{y1}bottom, 180°, g) → t3'_{y1}top
  117. Rotate(t4'_{y1}bottom, 180°, g) → t1'_{y1}top