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3D Rectangular Prism Demo

3D Rectangular Prism Demo
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2016-05-09 23:59
Solid GeometryGeometric Construction
This example demonstrates the manipulation of a 3D rectangular prism by adjusting its length, width, and height via sliders. It covers core concepts in solid geometry, 3D shapes, volume calculations, and algebraic relationships. The construction utilizes GeoGebra commands like If, Prism, and Sequence, along with objects such as height, length, width, and various faces/edges. Ideal for high school students and educators exploring 3D geometry, function-graphics correlations, and spatial reasoning skills.

GeoGebra Commands & Parameters

  1. If(HS ≥ 12, Text[floor(HS / 12)], "") → Hint
  2. If(WS ≥ 12, Text[floor(WS / 12)], "") → Wint
  3. If(LS ≥ 12, Text[floor(LS / 12)], "") → Lint
  4. If((WS - (floor(WS / 12) * 12)) / 12 ≟ 0, "", FractionText[(WS - (floor(WS / 12) * 12)) / 12]) → Wfrac
  5. Prism(Polygon[A, B, D, C], E) → a, F, edgeBF, edgeDG, edgeCH, edgeEF, edgeFG, edgeGH, edgeEH, G, H, faceABFE, faceBDGF, faceCDGH, faceACHE, faceEFGH, edgeAE
  6. Sequence(Segment[(i, 0, height), (i, width, height)], i, 0, floor(length)) → list1
  7. Sequence(Segment[(i, 0, 0), (i, 0, height)], i, 0, floor(length)) → list2
  8. Sequence(Segment[(length, i, 0), (length, i, height)], i, 0, floor(width)) → list3
  9. Sequence(Segment[(0, 0, i), (length, 0, i)], i, 0, floor(height)) → list4
  10. Sequence(Segment[(length, 0, i), (length, width, i)], i, 0, floor(height)) → list5
  11. Sequence(Segment[(0, i, height), (length, i, height)], i, 0, floor(width)) → list6
  12. Sequence(Segment[(0, 0, i), (0, width, i)], i, 0, floor(height)) → list7
  13. Sequence(Segment[(0, width, i), (length, width, i)], i, 0, floor(height)) → list8
  14. Sequence(Segment[(0, i, 0), (0, i, height)], i, 0, floor(width)) → list9
  15. Sequence(Segment[(i, width, 0), (i, width, height)], i, 0, floor(length)) → list10
  16. Sequence(Segment[(0, i, 0), (length, i, 0)], i, 0, floor(width)) → list11
  17. Sequence(Segment[(i, width, 0), (i, 0, 0)], i, 0, floor(length)) → list12
  18. If(b, 12, 1) → skips

AI Drawing Prompt Reference

Draw a 3D rectangular prism controlled by three sliders for length, width, and height. Show all faces and edges of the prism, with hint texts appearing when slider values exceed 12. Start by drawing the bottom and top faces, then connect corresponding edges to form the sides. Finally, use lines to represent the internal structure and intersections of the faces, ensuring a clear and complete visual representation.
The prompt above was compiled from the original drawing commands and is for reference only.