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立方体分割演示 by Diego Lieban (4)

立方体分割演示 by Diego Lieban (4)
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2018-12-09 03:29
立体几何微积分导数极限几何作图
①本范例演示如何通过旋转和相交操作将立方体分割成特定几何体；②涉及核心数学概念包括立体几何、导数、极限、等边三角形、集合论；③作图要点运用了Intersect（相交）、Point（点）、Cube（立方体）、Pyramid（金字塔）、Rotate（旋转）、Line（线）等GeoGebra命令；④适合高中及以上学生用于理解空间几何构造与微积分概念。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF_1, edgeFG, edgeCG_1, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Pyramid(A, C, D, G) → d, faceACD, edgeDG, faceACG, faceCDG, faceADG, edgeAC, edgeCD, edgeAD, edgeAG, edgeCG
  6. Pyramid(B, C, A, G) → b, faceABC, edgeAG_1, faceBCG, faceACG_1, faceABG, edgeBC, edgeAC_1, edgeAB, edgeBG, edgeCG_2
  7. Rotate(b, (-(90°)), edgeGH) → b_1
  8. Rotate(b_1, 90°, edgeCG) → b_2
  9. Rotate(b, If[0 < c ≤ 1, (-(((c * 90))°))], edgeGH) → b_{01}
  10. Rotate(b_1, If[1 < c ≤ 2, (((c - 1) * 90))°], edgeCG_2) → b_{12}
  11. Rotate(b_2, If[2 < c ≤ 3, (((c - 2) * 90))°], edgeFG) → b_{23}
  12. Rotate(b_2, 90°, edgeFG) → b_3
  13. Rotate(b_3, (-(90°)), edgeGH) → b_4
  14. Rotate(b_3, If[3 < c ≤ 4, (((-(c - 3)) * 90))°], edgeGH) → b_{34}
  15. Rotate(d, (-(90°)), edgeGH) → d_1
  16. Rotate(d_1, 90°, edgeCG) → d_2
  17. Rotate(d_2, 90°, edgeFG) → d_3
  18. Rotate(d_3, (-(90°)), edgeGH) → d_4
  19. Rotate(d, If[4 < c ≤ 5, (-(((c * 90))°))], edgeGH) → d_{01}
  20. Rotate(d_1, If[5 < c ≤ 6, (((c - 1) * 90))°], edgeCG_2) → d_{12}
  21. Rotate(d_2, If[6 < c ≤ 7, (((c - 2) * 90))°], edgeFG) → d_{23}
  22. Rotate(d_3, If[7 < c ≤ 8, (((-(c - 7)) * 90))°], edgeGH) → d_{34}
  23. Line(G, H) → r_1
  24. Line(C, G) → r_2
  25. Line(F, G) → r_3
  26. Line(G, H) → r_4