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Volume and Capacity: Packing Problem

Volume and Capacity: Packing Problem
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2021-10-12 12:28
VectorFunctionCoordinate GeometrySolid GeometryOptimization
This example demonstrates how to simulate and calculate the packing of different shaped objects using GeoGebra. It involves core mathematical concepts such as volume calculation, random variables, logarithmic functions, and parabolas. The construction utilizes commands and objects like Translate, Vector, Segment, Textfield, Sequence, CornerThreeD, and Element in GeoGebra. Suitable for high school students and teachers for learning and teaching purposes.

GeoGebra Commands & Parameters

  1. Translate(Prism[Polygon[A, A + (l, 0), A + (l, (-w)), A + (0, (-w))], (-h)], Vector[(0, 0)]) → a
  2. Vector((l', 0, 0)) → u1
  3. Segment(A + (l, 0, 0), A + (l, 0, h)) → f
  4. Segment(A + (0, (-w), 0), A + (l, (-w), 0)) → i
  5. Textfield(l) → InputBox1
  6. Textfield(w) → InputBox2
  7. Textfield(h) → InputBox3
  8. Segment(A + (l, 0, 0), A + (l, (-w), 0)) → g
  9. Textfield(l') → InputBox1_{1}
  10. Textfield(w') → InputBox2_{1}
  11. Textfield(h') → InputBox3_{1}
  12. Translate(Prism[Polygon[A, A + ((If[countlength ≟ 0, 1, countlength] * l'), 0), A + ((If[countlength ≟ 0, 1, countlength] * l'), ((-countwidth) * w')), A + (0, ((-countwidth) * w'))], ((-countheight) * h')], Vector[(0, 0)]) → b
  13. Sequence(Segment[A + ((p * l'), 0, (countheight * h')), A + ((p * l'), ((-countwidth) * w'), (countheight * h'))], p, 0, countlength) → l1
  14. Sequence(Segment[A + (0, ((-p) * w'), (countheight * h')), A + ((countlength * l'), ((-p) * w'), (countheight * h'))], p, 0, countwidth) → l2
  15. Sequence(Segment[A + ((p * l'), ((-countwidth) * w'), 0), A + ((p * l'), ((-countwidth) * w'), (countheight * h'))], p, 0, countlength) → l3
  16. Sequence(Segment[A + ((countlength * l'), ((-p) * w'), 0), A + ((countlength * l'), ((-p) * w'), (countheight * h'))], p, 0, countwidth) → l4
  17. Sequence(Segment[A + (0, ((-countwidth) * w'), (p * h')), A + ((countlength * l'), ((-countwidth) * w'), (p * h'))], p, 0, countheight) → l5
  18. Sequence(Segment[A + ((countlength * l'), 0, (p * h')), A + ((countlength * l'), ((-countwidth) * w'), (p * h'))], p, 0, countheight) → l6
  19. Sequence(Segment[A + ((p * l'), 0, 0), A + ((p * l'), ((-countwidth) * w'), 0)], p, 0, countlength) → l7
  20. Sequence(Segment[A + (0, ((-p) * w'), 0), A + ((countlength * l'), ((-p) * w'), 0)], p, 0, countwidth) → l8
  21. Sequence(Segment[A + ((p * l'), 0, 0), A + ((p * l'), 0, (countheight * h'))], p, 0, countlength) → l9
  22. Sequence(Segment[A + (0, 0, (p * h')), A + ((countlength * l'), 0, (p * h'))], p, 0, countheight) → l10
  23. Sequence(Segment[A + (0, ((-p) * w'), 0), A + (0, ((-p) * w'), (countheight * h'))], p, 0, countwidth) → l11
  24. Sequence(Segment[A + (0, 0, (p * h')), A + (0, ((-countwidth) * w'), (p * h'))], p, 0, countheight) → l12
  25. CornerThreeD(-1, 1) → C1
  26. CornerThreeD(-1, 7) → C7
  27. Translate(Prism[Polygon[A, A + (l', 0), A + (l', (-w')), A + (0, (-w'))], (-h')], Vector[(d, 0)]) → b'
  28. Element(lxmax, n') → xmax
  29. Element(lxmin, n') → xmin
  30. Element(lymax, n') → ymax
  31. Element(lymin, n') → ymin
  32. Element(lzmax, n') → zmax
  33. Element(lzmin, n') → zmin
  34. Segment(A + (d, (-w'), 0), A + (d + l', (-w'), 0)) → j
  35. Segment(A + (d + l', (-w'), 0), A + (d + l', 0, 0)) → k
  36. Segment(A + (d + l', 0, 0), A + (d + l', 0, h')) → m

AI Drawing Prompt Reference

Draw a 3D packing scene: on the left, a large rectangular box container with dimensions controlled by three input fields; on the right, a grid array of smaller rectangular boxes, each with its own dimensions set by three other input fields, arranged in rows, columns, and layers determined by count variables. A translation vector connects the large container and the small array, indicating the array can be moved. Inside the small array, draw grid lines using segments to form a clear 3D lattice structure. The overall scene illustrates a volume and capacity packing problem, emphasizing the relationship between size parameters and spatial arrangement.
The prompt above was compiled from the original drawing commands and is for reference only.