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Doubling a Cube

Doubling a Cube
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2019-12-03 04:20
VectorTransformationGeometric Construction
In collections Cuboids & their Nets
This example demonstrates the problem of doubling a cube, i.e., finding the edge length of a cube whose volume is twice that of a given cube using geometric methods. Key mathematical concepts include geometric construction, transformation, and vectors. Using GeoGebra commands such as Segment, Dilate, and LineBisector, the required geometric figures can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(D, A) → f
  2. Segment(A, C) → g
  3. Segment(C, C_1) → h
  4. Segment(C_1, D) → i
  5. Dilate(D, 1 / 3, A) → D'
  6. Dilate(D, 2 / 3, A) → D'_1
  7. Dilate(C_1, 1 / 3, C) → C'
  8. Dilate(C_1, 2 / 3, C) → C'_1
  9. Segment(D'_1, C'_1) → j
  10. Segment(D', C') → k
  11. Dilate(C, b, C_1) → B'
  12. LineBisector(A, B') → l
  13. Mirror(D', l) → D''
  14. Intersect(l, i) → E
  15. Intersect(l, g) → F
  16. Segment(D, E) → m
  17. Segment(A, F) → n
  18. Segment(F, C) → p
  19. Segment(E, C_1) → q
  20. Mirror(D, l) → D'_2
  21. Mirror(D, l) → D'_3
  22. Mirror(E, l) → E'
  23. Segment(D'_3, E') → m'
  24. Mirror(D, l) → D'_4
  25. Mirror(A, l) → A'
  26. Segment(D'_4, A') → f'
  27. Intersect(l, j) → G
  28. Intersect(l, k) → H
  29. Segment(D'_1, G) → r
  30. Segment(G, C'_1) → s
  31. Segment(D', H) → t
  32. Segment(H, C') → c
  33. Mirror(D'_1, l) → I
  34. Mirror(G, l) → G'
  35. Segment(I, G') → r'
  36. Mirror(D', l) → D''_1
  37. Mirror(H, l) → H'
  38. Segment(D''_1, H') → t'
  39. Mirror(A, l) → A'_1
  40. Mirror(F, l) → F'
  41. Segment(A'_1, F') → n'
  42. Intersect(c, n') → J
  43. Segment(H, J) → d
  44. Segment(J, C') → e
  45. Segment(G, D'') → f_1
  46. Segment(D'', C'_1) → g_1
  47. Intersect(q, f') → K
  48. Segment(E, K) → h_1
  49. Segment(K, C_1) → i_1
  50. Segment(F, A) → j_1
  51. Segment(A, D) → k_1
  52. Segment(D, E') → l_1