立方体下方的金字塔体积计算方法

立方体下方的金字塔体积计算方法
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2019-07-29 11:51
①本范例演示了如何在立方体下方构造金字塔并计算其体积;②涉及的核心数学概念包括体积公式、立体几何、对称性、向量运算;③作图要点——使用了GeoGebra命令/对象:Cube(立方体)、Line(线)、Rotate(旋转)、Segment(线段)、Midpoint(中点)、Pyramid(金字塔)、Vector(向量)、Translate(平移);④适合高中阶段学习立体几何和体积计算的学生,也可用于数学教学演示。

GeoGebra 命令及参数

  1. Cube(A, B, C) → cube, D, faceCDHG_1, faceEFGH_1, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD_1, faceADHE_1, faceABFE_1, faceBCGF_1
  2. Line(A, B) → ax1
  3. Rotate(E, fold_unfold, ax1) → E'
  4. Line(E, F) → ax5
  5. Segment(G, A) → f
  6. Midpoint(f) → O
  7. Pyramid(E, F, G, H, O) → Pyr5, faceEFGH, edgecenterE_2, edgecenterF_2, edgecenterG_1, edgecenterH_1, facecenterEF, facecenterFG_1, facecenterGH_1, facecenterEH_1, edgeEF, edgeFG_2, edgeGH_2, edgeEH_2
  8. Pyramid(A, E, F, B, O) → Pyr1, faceABFE, edgeAcenter_1, edgecenterE_1, edgecenterF_1, edgeBcenter_1, faceAcenterE_1, facecenterEF_1, faceBcenterF_1, faceABcenter_1, edgeAE_2, edgeEF_2, edgeBF_2, edgeAB_2
  9. Rotate(Pyr1, fold_unfold, ax1) → Rot1
  10. Vector(E, E') → u
  11. Translate(Rotate[Pyr5, (2 * fold_unfold), ax5], u) → Rot5
  12. Pyramid(B, C, G, F, O) → Pyr2, faceBCGF, edgeBcenter_2, edgeCcenter_1, edgecenterG_2, edgecenterF, faceBCcenter_1, faceCcenterG_1, facecenterFG, faceBcenterF, edgeBC_2, edgeCG_2, edgeFG, edgeBF
  13. Line(B, C) → ax2
  14. Rotate(Pyr2, fold_unfold, ax2) → Rot2
  15. Pyramid(C, D, H, G, O) → Pyr3, faceCDHG, edgeCcenter_2, edgecenterD_1, edgecenterH_2, edgecenterG, faceCcenterD_1, facecenterDH_1, facecenterGH, faceCcenterG, edgeCD_2, edgeDH_2, edgeGH, edgeCG
  16. Line(C, D) → ax3
  17. Rotate(Pyr3, fold_unfold, ax3) → Rot3
  18. Pyramid(D, A, E, H, O) → Pyr4, faceADHE, edgecenterD_2, edgeAcenter_2, edgecenterE, edgecenterH, faceAcenterD_1, faceAcenterE, facecenterEH, facecenterDH, edgeAD_2, edgeAE, edgeEH, edgeDH
  19. Line(D, A) → ax4
  20. Rotate(Pyr4, fold_unfold, ax4) → Rot4
  21. Pyramid(A, B, C, D, O) → Pyr6, faceABCD, edgeAcenter, edgeBcenter, edgeCcenter, edgecenterD, faceABcenter, faceBCcenter, faceCcenterD, faceAcenterD, edgeAB, edgeBC, edgeCD, edgeAD

AI 绘图提示语参考

画一个立方体,然后在其顶面中心绘制一个点,连接顶面四个顶点与该点形成四个锥体,再将这四个锥体沿立方体各边翻转并平移到立方体下方对应位置,最终形成六个锥体与立方体组合的立体图形,展示体积计算方法。
以上提示语为根据原始绘图命令整理而来,仅供参考。