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Paper Folding Doubling The Cube

Paper Folding Doubling The Cube
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2018-04-24 10:19
Solid GeometryTransformationGeometric Construction
This example demonstrates how to construct a cube with double the volume through paper folding. It involves core mathematical concepts such as cubes, tangent functions, logarithmic functions, dilation, general quadrilaterals, and circumcircles. The construction uses GeoGebra commands like Segment, Dilate, LineBisector, Mirror, and Intersect. Suitable for high school students and geometry enthusiasts to understand geometric constructions and transformations in solving mathematical problems.

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