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分数边长立方体打包

分数边长立方体打包
几何画板及绘图内容加载中，请稍等……
2018-01-05 00:25
数列立体几何概率统计
①本范例演示了不同分数边长的立方体打包排列现象；②涉及核心数学概念包括数列、概率统计、立体几何和期望值；③作图要点使用了RandomElement, Sequence, Random, Surface, Prism等GeoGebra命令和对象；④适合高中及以上数学教学或几何探究。

GeoGebra 命令及参数

  1. RandomElement({3, 5, 7, 9, 11, 13}) → a
  2. Sequence(Plane[x + (0 * z) = k], k, 1, a, 1) → list2
  3. RandomElement({3, 5, 7, 9, 11, 13}) → b
  4. Sequence(Plane[y + (0 * z) = k], k, 1, b, 1) → list1
  5. Random(3, 10) → h
  6. Surface(j, k, h, j, 0, a, k, 0, b) → d
  7. Surface(j, k, 0, j, 0, a, k, 0, b) → A2
  8. Prism(A, B, C, D, A, E) → e, F, faceAAEI, faceEFGHI, edgeAB, edgeBC, edgeCD, edgeAD, edgeAA, edgeAE, edgeBF, edgeCG, G, edgeDH, edgeAI, edgeEF, edgeFG, edgeGH, edgeHI, edgeEI, H, I, faceAADCB, faceABFE, faceBCGF, faceCDHG, faceADHI
  9. Random(0, 10) → c
  10. Random(1, 13) → a_1
  11. Random(1, 13) → b_1
  12. Surface(j, k, C2 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G2
  13. Surface(j, k, C3 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G3
  14. Surface(j, k, C4 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G4
  15. Surface(j, k, C5 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G5
  16. Surface(j, k, C6 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G6
  17. Surface(j, k, C7 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G7
  18. Surface(j, k, C8 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G8
  19. Surface(j, k, C9 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G9
  20. Surface(j, k, C10 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G10
  21. Surface(j, k, C11 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G11
  22. Surface(j, k, C12 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G12
  23. Surface(j, k, C13 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G13
  24. Surface(j, k, C14 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G14
  25. Surface(j, k, C15 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G15
  26. Surface(j, k, C16 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G16
  27. Surface(j, k, C17 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G17
  28. Surface(j, k, C18 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G18
  29. Surface(j, k, C19 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G19
  30. Surface(j, k, C20 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G20
  31. Surface(j, k, C21 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G21
  32. Surface(j, k, C22 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G22
  33. Surface(j, k, C23 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G23
  34. Surface(j, k, C24 / n, j, -0.03, (u * row) + 0.03, k, -0.1, (u * col) + 0.03) → G24
  35. Surface(C1, k, j, j, -0.05, (u * layer) + 0.015, k, -0.05, (u * col) + 0.05) → H1
  36. Surface(C2, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H2
  37. Surface(C3, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H3
  38. Surface(C4, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H4
  39. Surface(C5, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H5
  40. Surface(C6, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H6
  41. Surface(C7, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H7
  42. Surface(C8, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H8
  43. Surface(C9, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H9
  44. Surface(C10, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H10
  45. Surface(C11, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H11
  46. Surface(C12, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H12
  47. Surface(C13, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H13
  48. Surface(C14, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H14
  49. Surface(C15, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H15
  50. Surface(C16, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H16
  51. Surface(C17, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H17
  52. Surface(C18, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H18
  53. Surface(C19, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H19
  54. Surface(C20, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H20
  55. Surface(C21, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H21
  56. Surface(C22, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H22
  57. Surface(C23, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H23
  58. Surface(C24, k, j, j, -0.0500000000000002, (u * layer) + 0.015, k, -0.0500000000000002, (u * col) + 0.0500000000000002) → H24
  59. Surface(j, C1 - 0.01, k, j, 0, (u * row) + 0.05, k, 0, (u * layer) + 0.05) → I1
  60. Surface(j, C2 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I2
  61. Surface(j, C3 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I3
  62. Surface(j, C4 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I4
  63. Surface(j, C5 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I5
  64. Surface(j, C6 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I6
  65. Surface(j, C7 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I7
  66. Surface(j, C8 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I8
  67. Surface(j, C9 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I9
  68. Surface(j, C10 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I10
  69. Surface(j, C11 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I11
  70. Surface(j, C12 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I12
  71. Surface(j, C13 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I13
  72. Surface(j, C14 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I14
  73. Surface(j, C15 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I15
  74. Surface(j, C16 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I16
  75. Surface(j, C17 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I17
  76. Surface(j, C18 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I18
  77. Surface(j, C19 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I19
  78. Surface(j, C20 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I20
  79. Surface(j, C21 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I21
  80. Surface(j, C22 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I22
  81. Surface(j, C23 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I23
  82. Surface(j, C24 - 0.01, k, j, 0, (u * row) + 0.0500000000000002, k, 0, (u * layer) + 0.0500000000000002) → I24
  83. Surface(j, k, (u * C2) - 0.05, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D2
  84. Surface(j, k, (u * C3) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D3
  85. Surface(j, k, (u * C4) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D4
  86. Surface(j, k, (u * C5) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D5
  87. Surface(j, k, (u * C6) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D6
  88. Surface(j, k, (u * C7) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D7
  89. Surface(j, k, (u * C8) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D8
  90. Surface(j, k, (u * C9) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D9
  91. Surface(j, k, (u * C10) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D10
  92. Surface(j, k, (u * C11) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D11
  93. Surface(j, k, (u * C12) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D12
  94. Surface(j, k, (u * C13) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D13
  95. Surface(j, k, (u * C14) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D14
  96. Surface(j, k, (u * C15) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D15
  97. Surface(j, k, (u * C16) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D16
  98. Surface(j, k, (u * C17) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D17
  99. Surface(j, k, (u * C18) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D18
  100. Surface(j, k, (u * C19) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D19
  101. Surface(j, k, (u * C20) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D20
  102. Surface(j, k, (u * C21) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D21
  103. Surface(j, k, (u * C22) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D22
  104. Surface(j, k, (u * C23) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D23
  105. Surface(j, k, (u * C24) - 0.0500000000000002, j, -0.1, (u * row) + 0.1, k, -0.1, (u * col) + 0.1) → D24
  106. Surface((u * (C1 + 1)) + 0.05, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E2
  107. Surface((u * (C2 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E3
  108. Surface((u * (C3 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E4
  109. Surface((u * (C4 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E5
  110. Surface((u * (C5 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E6
  111. Surface((u * (C6 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E7
  112. Surface((u * (C7 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E8
  113. Surface((u * (C8 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E9
  114. Surface((u * (C9 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E10
  115. Surface((u * (C10 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E11
  116. Surface((u * (C11 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E12
  117. Surface((u * (C12 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E13
  118. Surface((u * (C13 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E14
  119. Surface((u * (C14 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E15
  120. Surface((u * (C15 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E16
  121. Surface((u * (C16 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E17
  122. Surface((u * (C17 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E18
  123. Surface((u * (C18 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E19
  124. Surface((u * (C19 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E20
  125. Surface((u * (C20 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E21
  126. Surface((u * (C21 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E22
  127. Surface((u * (C22 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E23
  128. Surface((u * (C23 + 1)) + 0.0500000000000002, k, j, j, -0.1, (u * layer) + 0.015, k, -0.1, (u * col) + 0.1) → E24
  129. Surface(j, (u * C1), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F2
  130. Surface(j, (u * C2), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F3
  131. Surface(j, (u * C3), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F4
  132. Surface(j, (u * C4), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F5
  133. Surface(j, (u * C5), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F6
  134. Surface(j, (u * C6), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F7
  135. Surface(j, (u * C7), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F8
  136. Surface(j, (u * C8), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F9
  137. Surface(j, (u * C9), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F10
  138. Surface(j, (u * C10), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F11
  139. Surface(j, (u * C11), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F12
  140. Surface(j, (u * C12), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F13
  141. Surface(j, (u * C13), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F14
  142. Surface(j, (u * C14), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F15
  143. Surface(j, (u * C15), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F16
  144. Surface(j, (u * C16), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F17
  145. Surface(j, (u * C17), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F18
  146. Surface(j, (u * C18), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F19
  147. Surface(j, (u * C19), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F20
  148. Surface(j, (u * C20), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F21
  149. Surface(j, (u * C21), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F22
  150. Surface(j, (u * C22), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F23
  151. Surface(j, (u * C23), k, j, 0, (u * row) + 0.1, k, 0, (u * layer) + 0.1) → F24

AI 绘图提示语参考

绘制一个三维立体图形，展示不同分数边长的小立方体在网格中的随机堆叠。首先，在水平面上生成一个由随机数量的平行平面划分的矩形网格，网格的行数和列数分别从奇数集合中随机选取。然后，在网格上方随机高度处放置一个水平顶面，形成一个大立方体的框架。接着，在网格的每个单元格中，随机生成多个小立方体，每个小立方体的高度由随机分数决定，并沿垂直方向逐层堆叠，形成高低错落的柱状结构。整体呈现为一种基于概率的立体填充效果，适合用于数学教学中的几何与统计演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。