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Pyramids in Prism

Pyramids in Prism
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2017-08-30 13:24
TrigonometrySolid GeometryGeometric Construction
This example demonstrates carving a rectangular prism into three congruent rectangular pyramids. It involves core concepts like solid geometry, volume calculations, congruent triangles, and ratios. The construction uses commands such as Intersect, Point, Translate, Segment, Pyramid, Rotate, and Line in GeoGebra. Suitable for high school geometry education or math clubs.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Ray[A, A + (1, 0)]) → B
  3. Point(Ray[A, A + (0, 1)]) → C
  4. Translate(A, Vector[(0, 0, ht)]) → A'
  5. Translate(B, Vector[(0, 0, ht)]) → B'
  6. Translate(C, Vector[(0, 0, ht)]) → C'
  7. Translate(D, Vector[(0, 0, ht)]) → D'
  8. Segment(A, A') → a
  9. Segment(B, B') → b
  10. Segment(C, C') → c
  11. Segment(D, D') → d
  12. Segment(A, B) → e
  13. Segment(D, C) → f
  14. Segment(B, D) → g
  15. Segment(C, A) → h
  16. Segment(A', B') → i
  17. Segment(B', D') → j
  18. Segment(D', C') → k
  19. Segment(C', A') → l
  20. Pyramid(A, B, B', A', C') → m, faceAA'B'B, edgeAC'_1, edgeBC'_1, edgeB'C'_1, edgeA'C', faceABC'_1, faceBB'C'_1, faceA'B'C', faceAA'C', edgeAB_1, edgeBB'_1, edgeA'B', edgeAA'
  21. Pyramid(A, B, D, C, C') → n, faceABDC, edgeAC', edgeBC'_2, edgeC'D_1, edgeCC', faceABC', faceBC'D_1, faceCC'D, faceACC', edgeAB_2, edgeBD_1, edgeCD, edgeAC
  22. Pyramid(B, D, D', B', C') → o, faceBB'D'D, edgeBC', edgeC'D, edgeC'D', edgeB'C', faceBC'D, faceC'DD', faceB'C'D', faceBB'C', edgeBD_2, edgeDD', edgeB'D', edgeBB'
  23. Rotate
  24. Rotate
  25. Line(A, B) → q
  26. Rotate
  27. Rotate
  28. Rotate(A', ((decompose * 90))°, A, Vector[A, B]) → A''
  29. Rotate(B', ((decompose * 90))°, A, Vector[A, B]) → B''
  30. Rotate(C', ((decompose * 90))°, A, Vector[A, B]) → C''
  31. Pyramid(A, B, B'', A'', C'') → r, faceAA''B''B, edgeAC'', edgeBC'', edgeB''C'', edgeA''C'', faceABC'', faceBB''C'', faceA''B''C'', faceAA''C'', edgeAB, edgeBB'', edgeA''B'', edgeAA''
  32. Rotate(B', ((decompose * 90))°, B, Vector[B, D]) → B''_1
  33. Rotate(D', ((decompose * 90))°, B, Vector[B, D]) → D''
  34. Rotate(C', ((decompose * 90))°, B, Vector[B, D]) → C''_1
  35. Pyramid(B, D, D'', B''_1, C''_1) → s, face5, edge2, edge3, edge6, edge5, face1, face3, face4, face2, edgeBD, edgeDD'', edge4, edge1

AI Drawing Prompt Reference

Draw a rectangular prism and carve it into three congruent rectangular pyramids, showing the cutting process and results, emphasizing volume calculations, congruent triangles, and ratios, start by drawing the prism and cutting lines, then construct the pyramids step by step, and finally rotate parts of the pyramids to show spatial relationships.
The prompt above was compiled from the original drawing commands and is for reference only.