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棱柱分割成三个矩形金字塔

棱柱分割成三个矩形金字塔
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2017-08-30 13:24
三角函数立体几何几何作图
①本范例演示将一个矩形棱柱分割成三个矩形金字塔的过程；②涉及的核心数学概念包括立体几何、体积计算、全等三角形、比例关系；③作图要点——从下方『构造摘要』提炼用到了Intersect（相交）、Point（点）、Translate（平移）、Segment（线段）、Pyramid（金字塔）、Rotate（旋转）、Line（直线）等GeoGebra命令/对象；④适合高中立体几何教学或数学兴趣小组使用。

GeoGebra 命令及参数

  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 绘图提示语参考

画一个长方体，将其切割成三个全等的矩形金字塔，展示切割过程和结果，强调体积计算、全等三角形和比例关系，先画出长方体和切割线，再逐步构建金字塔，最后旋转部分金字塔展示空间关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。