MathPlotAI Logo MathPlotAI

Cube Packing Demonstration

Cube Packing Demonstration
Loading the math board and drawing, please wait…
2015-04-21 01:49
FunctionSolid GeometryGeometric Construction
This interactive tool demonstrates how to pack a right rectangular prism with smaller cubes, covering core math concepts like volume calculation, functions, equations, and geometric constructions. It utilizes GeoGebra commands such as Random, Sequence, Surface, and Prism to create the model, making it suitable for upper elementary and middle school students learning solid geometry and spatial reasoning.

GeoGebra Commands & Parameters

  1. Random(1, 13) → a
  2. Sequence(Plane[x + (0 * z) = k], k, 1, a, 1) → list2
  3. Random(1, 13) → b
  4. Sequence(Plane[y + (0 * z) = k], k, 1, b, 1) → list1
  5. Random(1, 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. Surface(j, k, C2 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D2
  9. Surface(j, k, C3 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D3
  10. Surface(j, k, C4 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D4
  11. Surface(j, k, C5 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D5
  12. Surface(j, k, C6 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D6
  13. Surface(j, k, C7 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D7
  14. Surface(j, k, C8 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D8
  15. Surface(j, k, C9 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D9
  16. Surface(j, k, C10 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D10
  17. Surface(j, k, C11 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D11
  18. Surface(j, k, C12 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D12
  19. Surface(j, k, C13 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D13
  20. Surface(j, k, C14 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D14
  21. Surface(j, k, C15 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D15
  22. Surface(j, k, C16 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D16
  23. Surface(j, k, C17 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D17
  24. Surface(j, k, C18 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D18
  25. Surface(j, k, C19 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D19
  26. Surface(j, k, C20 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D20
  27. Surface(j, k, C21 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D21
  28. Surface(j, k, C22 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D22
  29. Surface(j, k, C23 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D23
  30. Surface(j, k, C24 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D24
  31. 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
  32. Random(0, 10) → c
  33. Random(1, 13) → a_1
  34. Random(1, 13) → b_1
  35. Surface(j, C1, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F1
  36. Surface(j, C2, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F2
  37. Surface(j, C3, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F3
  38. Surface(j, C4, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F4
  39. Surface(j, C5, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F5
  40. Surface(j, C6, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F6
  41. Surface(j, C7, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F7
  42. Surface(j, C8, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F8
  43. Surface(j, C9, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F9
  44. Surface(j, C10, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F10
  45. Surface(j, C11, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F11
  46. Surface(j, C12, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F12
  47. Surface(j, C13, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F13
  48. Surface(j, C14, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F14
  49. Surface(j, C15, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F15
  50. Surface(j, C16, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F16
  51. Surface(j, C17, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F17
  52. Surface(j, C18, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F18
  53. Surface(j, C19, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F19
  54. Surface(j, C20, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F20
  55. Surface(j, C21, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F21
  56. Surface(j, C22, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F22
  57. Surface(j, C23, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F23
  58. Surface(j, C24, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F24
  59. Surface(C1, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E1
  60. Surface(C2, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E2
  61. Surface(C3, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E3
  62. Surface(C4, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E4
  63. Surface(C5, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E5
  64. Surface(C6, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E6
  65. Surface(C7, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E7
  66. Surface(C8, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E8
  67. Surface(C9, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E9
  68. Surface(C10, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E10
  69. Surface(C11, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E11
  70. Surface(C12, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E12
  71. Surface(C13, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E13
  72. Surface(C14, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E14
  73. Surface(C15, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E15
  74. Surface(C16, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E16
  75. Surface(C17, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E17
  76. Surface(C18, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E18
  77. Surface(C19, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E19
  78. Surface(C20, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E20
  79. Surface(C21, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E21
  80. Surface(C22, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E22
  81. Surface(C23, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E23
  82. Surface(C24, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E24

AI Drawing Prompt Reference

Create a 3D demonstration of packing a rectangular prism with unit cubes. Randomly set the prism's length, width, and height (rows, columns, and layers). Draw a transparent rectangular container as the outer shell. Inside, fill the container layer by layer from bottom to top, with each layer containing a grid of small cubes aligned to the base rows and columns. Slightly offset each cube to show its edges clearly. Emphasize the spatial stacking and volume-filling concept.
The prompt above was compiled from the original drawing commands and is for reference only.