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Pyramids in Prism by Jaime Guerrero López

Pyramids in Prism by Jaime Guerrero López
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2015-11-15 04:00
Solid GeometryGeometric Construction
This example demonstrates how to carve a rectangular prism into three congruent rectangular pyramids. It involves core math concepts like volume calculation, geometric dissection, and solid geometry. Constructed using commands like Intersect, Point, Translate, Segment, Pyramid, Rotate, and Line. Suitable for high school students learning about solid geometry and volume calculations.

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, demonstrating volume calculation and geometric dissection. Start by constructing the base and sides of the prism, then translate and rotate to form the apex points of the pyramids, and finally connect the apexes to the base to create the pyramid faces, highlighting geometric construction and volume relationships.
The prompt above was compiled from the original drawing commands and is for reference only.