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立方体二等分 by Diego Lieban

立方体二等分 by Diego Lieban
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2019-02-20 22:27
解析几何立体几何几何作图
本范例展示了如何将立方体二等分。核心数学概念包括立体几何中的体积和表面积。通过使用GeoGebra命令如Point, Intersect, Cube, Line等，可以构造出立方体及其分割面。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Point(xAxis) → B
  2. Intersect(yAxis, xAxis) → A
  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_1, edgeEH, edgeEF, E, edgeBF_1, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD_1, faceADHE, faceABFE, faceBCGF
  5. Line(A, E) → i
  6. Sphere(A, g) → h
  7. Midpoint(H, B) → I
  8. Pyramid(A, D, C, B, I) → b, faceABCD, edgeAI_1, edgeDI_1, edgeCI_1, edgeBI_1, faceADI_1, faceCDI_1, faceBCI_1, faceABI_1, edgeAD_2, edgeCD_2, edgeBC_2, edgeAB_2
  9. Pyramid(F, C, B, I) → c, faceBCF, edgeBI_2, faceCFI, faceBCI, faceBFI_1, edgeCF, edgeBC, edgeBF_2, edgeFI_1, edgeCI_2
  10. Pyramid(F, B, A, I) → d, faceABF, edgeAI_2, faceBFI, faceABI, faceAFI, edgeBF, edgeAB, edgeAF, edgeFI, edgeBI
  11. Pyramid(A, H, D, I) → e, faceADH, edgeDI_2, faceAHI, faceDHI_1, faceADI, edgeAH, edgeDH_2, edgeAD, edgeAI, edgeHI_1
  12. Pyramid(C, D, H, I) → f, faceCDH, edgeHI, faceCDI, faceDHI, faceCHI, edgeCD, edgeDH, edgeCH, edgeCI, edgeDI
  13. Intersect(i, h) → J, K
  14. Vector(A, K) → u
  15. Translate(A, u) → A'
  16. Translate(b, u) → b'
  17. Translate(c, u) → c'
  18. Translate(d, u) → d'
  19. Translate(e, u) → e'
  20. Translate(f, u) → f'
  21. OrthogonalLine(I, xOyPlane) → j
  22. Rotate(b', α, j) → b''
  23. Rotate(c', α, j) → c''
  24. Rotate(d', α, j) → d''
  25. Rotate(e', α, j) → e''
  26. Rotate(f', α, j) → f''
  27. Line(H, F) → k
  28. Translate(I, u) → I'
  29. Line(I', k) → l
  30. Rotate(b'', β, l) → b'''
  31. Rotate(c'', β, l) → c'''
  32. Rotate(d'', β, l) → d'''
  33. Rotate(e'', β, l) → e'''
  34. Rotate(f'', β, l) → f'''
  35. Sphere(I', m) → n
  36. Intersect(j, n) → L, M
  37. Vector(I', L) → v
  38. Translate(b''', v) → b_f
  39. Translate(c''', v) → c_f
  40. Translate(d''', v) → d_f
  41. Translate(e''', v) → e_f
  42. Translate(f''', v) → f_f