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Divide a Cube into Two Equal Parts

Divide a Cube into Two Equal Parts
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2019-02-20 22:27
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to divide a cube into two equal parts. Key mathematical concepts include volume and surface area in solid geometry. Using GeoGebra commands such as Point, Intersect, Cube, Line, etc., the construction of the cube and its dividing faces is shown. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  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