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Paper Folding Fractions

Paper Folding Fractions
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2017-04-18 07:36
FunctionInequalityGeometric Construction
This example demonstrates the concept of fractions through paper folding. It involves mathematical concepts such as fractions, inequalities, and rotation. Using GeoGebra commands like Take, Reverse, Element, etc., a series of geometric shapes can be constructed. Suitable for students at the junior high school level and above to learn about fractions and geometric construction.

GeoGebra Commands & Parameters

  1. Take(Text[num], 3, Length[Text[num]]) → text1
  2. Reverse(list1) → list2
  3. Element(list2, A2) → B2
  4. Polygon((0, 0), (1, 0), (1, 0.2), (0, 0.2)) → poly1, f, g, h, i
  5. Textfield(num) → InputBox1
  6. Length(Text[num]) → a
  7. Element(list2, A1) → B1
  8. Element(list2, A3) → B3
  9. Element(list2, A4) → B4
  10. Element(list2, A5) → B5
  11. Element(list2, A6) → B6
  12. Element(list2, A7) → B7
  13. Element(list2, A8) → B8
  14. Element(list2, A9) → B9
  15. Element(list2, A10) → B10
  16. Element(list2, A11) → B11
  17. Element(list2, A12) → B12
  18. Element(list2, A13) → B13
  19. Element(list2, A14) → B14
  20. If(Defined[B2], If[B2 ≟ 1, Dilate[C1, dfactor, (1, 0)], Dilate[C1, dfactor, (0, 0)]], (NaN, NaN)) → C2
  21. Element(list2, A15) → B15
  22. If(Defined[B3], If[B3 ≟ 1, Dilate[C2, dfactor, (1, 0)], Dilate[C2, dfactor, (0, 0)]], (NaN, NaN)) → C3
  23. If(Defined[B4], If[B4 ≟ 1, Dilate[C3, dfactor, (1, 0)], Dilate[C3, dfactor, (0, 0)]], (NaN, NaN)) → C4
  24. If(Defined[B5], If[B5 ≟ 1, Dilate[C4, dfactor, (1, 0)], Dilate[C4, dfactor, (0, 0)]], (NaN, NaN)) → C5
  25. If(Defined[B6], If[B6 ≟ 1, Dilate[C5, dfactor, (1, 0)], Dilate[C5, dfactor, (0, 0)]], (NaN, NaN)) → C6
  26. If(Defined[B7], If[B7 ≟ 1, Dilate[C6, dfactor, (1, 0)], Dilate[C6, dfactor, (0, 0)]], (NaN, NaN)) → C7
  27. If(Defined[B8], If[B8 ≟ 1, Dilate[C7, dfactor, (1, 0)], Dilate[C7, dfactor, (0, 0)]], (NaN, NaN)) → C8
  28. If(Defined[B9], If[B9 ≟ 1, Dilate[C8, dfactor, (1, 0)], Dilate[C8, dfactor, (0, 0)]], (NaN, NaN)) → C9
  29. If(Defined[B10], If[B10 ≟ 1, Dilate[C9, dfactor, (1, 0)], Dilate[C9, dfactor, (0, 0)]], (NaN, NaN)) → C10
  30. If(Defined[B11], If[B11 ≟ 1, Dilate[C10, dfactor, (1, 0)], Dilate[C10, dfactor, (0, 0)]], (NaN, NaN)) → C11
  31. If(Defined[B12], If[B12 ≟ 1, Dilate[C11, dfactor, (1, 0)], Dilate[C11, dfactor, (0, 0)]], (NaN, NaN)) → C12
  32. If(Defined[B13], If[B13 ≟ 1, Dilate[C12, dfactor, (1, 0)], Dilate[C12, dfactor, (0, 0)]], (NaN, NaN)) → C13
  33. If(Defined[B14], If[B14 ≟ 1, Dilate[C13, dfactor, (1, 0)], Dilate[C13, dfactor, (0, 0)]], (NaN, NaN)) → C14
  34. If(Defined[B15], If[B15 ≟ 1, Dilate[C14, dfactor, (1, 0)], Dilate[C14, dfactor, (0, 0)]], (NaN, NaN)) → C15
  35. Segment(C1, C1 + (0, 0.2)) → D1
  36. Segment(C2, C2 + (0, 0.2)) → D2
  37. Segment(C3, C3 + (0, 0.2)) → D3
  38. Segment(C4, C4 + (0, 0.2)) → D4
  39. Segment(C5, C5 + (0, 0.2)) → D5
  40. Segment(C6, C6 + (0, 0.2)) → D6
  41. Segment(C7, C7 + (0, 0.2)) → D7
  42. Segment(C8, C8 + (0, 0.2)) → D8
  43. Segment(C9, C9 + (0, 0.2)) → D9
  44. Segment(C10, C10 + (0, 0.2)) → D10
  45. Segment(C11, C11 + (0, 0.2)) → D11
  46. Segment(C12, C12 + (0, 0.2)) → D12
  47. Segment(C13, C13 + (0, 0.2)) → D13
  48. Segment(C14, C14 + (0, 0.2)) → D14
  49. Segment(C15, C15 + (0, 0.2)) → D15
  50. RemoveUndefined(list3) → list4
  51. RemoveUndefined(list5) → list6
  52. Sequence(FractionText[x(Element[list6, t])], t, 1, Length[list6]) → list7
  53. Segment((0, 0), (0, 0.2)) → j
  54. Segment((1, 0), (1, 0.2)) → k
  55. Vector((1, 0.25), (0, 0.25)) → E1
  56. If(B2 ≟ 1, Vector[B, C1 + (0, 0.25)], Vector[A, C1 + (0, 0.25)]) → E2
  57. If(B4 ≟ 1, Vector[B, C3 + (0, 0.25)], Vector[A, C3 + (0, 0.25)]) → E4
  58. If(B5 ≟ 1, Vector[B, C4 + (0, 0.25)], Vector[A, C4 + (0, 0.25)]) → E5
  59. If(B6 ≟ 1, Vector[B, C5 + (0, 0.25)], Vector[A, C5 + (0, 0.25)]) → E6
  60. If(B3 ≟ 1, Vector[B, C2 + (0, 0.25)], Vector[A, C2 + (0, 0.25)]) → E3
  61. If(B7 ≟ 1, Vector[B, C6 + (0, 0.25)], Vector[A, C6 + (0, 0.25)]) → E7
  62. If(B8 ≟ 1, Vector[B, C7 + (0, 0.25)], Vector[A, C7 + (0, 0.25)]) → E8
  63. If(B9 ≟ 1, Vector[B, C8 + (0, 0.25)], Vector[A, C8 + (0, 0.25)]) → E9
  64. If(B10 ≟ 1, Vector[B, C9 + (0, 0.25)], Vector[A, C9 + (0, 0.25)]) → E10
  65. If(B11 ≟ 1, Vector[B, C10 + (0, 0.25)], Vector[A, C10 + (0, 0.25)]) → E11
  66. If(B12 ≟ 1, Vector[B, C11 + (0, 0.25)], Vector[A, C11 + (0, 0.25)]) → E12
  67. If(B13 ≟ 1, Vector[B, C12 + (0, 0.25)], Vector[A, C12 + (0, 0.25)]) → E13
  68. If(B14 ≟ 1, Vector[B, C13 + (0, 0.25)], Vector[A, C13 + (0, 0.25)]) → E14
  69. If(B15 ≟ 1, Vector[B, C14 + (0, 0.25)], Vector[A, C14 + (0, 0.25)]) → E15