积极 AI Logo 积极 AI

三等分立方体为三个金字塔

三等分立方体为三个金字塔
几何画板及绘图内容加载中，请稍等……
2018-09-14 19:27
向量立体几何几何作图
①本范例演示如何将一个立方体三等分为三个金字塔形；②涉及的核心数学概念包括立体几何、体积计算、空间变换；③作图要点——从下方『构造摘要』提炼用到了If、Cube、Pyramid、Rotate、Midpoint、OrthogonalLine、Segment等GeoGebra命令/对象；④适合高中及以上学生学习和探索空间几何问题，也可用于数学教学演示。

GeoGebra 命令及参数

  1. If(t < 0.5, (2 * t), 1) → t1
  2. Cube(A, B, xOyPlane) → a, C, faceBCGF, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH_1, edgeEH_1, D, edgeEF, edgeBF, edgeFG, edgeCG, edgeGH_1, E, F, G, H, faceABCD, faceADHE, faceABFE
  3. Pyramid(faceABCD, H) → b, faceADH, faceABH_1, faceBCH_1, faceCDH, edgeDH, edgeAH_1, edgeBH_1, edgeCH_1
  4. Pyramid(faceBCGF, H) → c, faceBCH, faceBFH_1, faceFGH, faceCGH, edgeCH, edgeBH_2, edgeFH_1, edgeGH
  5. Pyramid(faceABFE, H) → d, faceABH, faceAEH, faceEFH, faceBFH, edgeBH, edgeAH, edgeEH, edgeFH
  6. Rotate(E, (90° * t1), edgeAB) → E'
  7. Midpoint(E', B) → I
  8. OrthogonalLine(I, Polygon[A, I, B]) → e
  9. Rotate(G, (90° * t1), edgeBC) → G'
  10. Midpoint(B, G') → J
  11. OrthogonalLine(J, Polygon[B, C, G']) → f
  12. Rotate(Pyramid[faceABCD, H], 0*°, edgeDH) → b'
  13. If(t ≥ 0.5, (2 * (t - 0.5)), 0) → t2
  14. Rotate(Rotate[c, (90° * t1), edgeBC], (-((90° * t2))), f) → c'
  15. Rotate(Rotate[d, (90° * t1), edgeAB], (((-90))° * t2), e) → d'
  16. Segment(A, B) → g
  17. Segment(B, C) → h
  18. Segment(C, D) → i
  19. Segment(D, A) → j
  20. Segment(A, E) → k
  21. Segment(B, F) → l
  22. Segment(C, G) → m
  23. Segment(D, H) → n
  24. Segment(E, F) → p
  25. Segment(F, G) → q
  26. Segment(G, H) → r
  27. Segment(H, E) → s