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Fraction and Geometry Transformation Demo

Fraction and Geometry Transformation Demo
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2015-07-14 16:56
PolygonTrigonometrySequenceGeometric ConstructionSlider Animation
This example dynamically demonstrates the geometric transformation of fractions and small polygons, intuitively showing the relationship between similarity transformation and fraction operations. It involves core math concepts like fractions, similarity transformation, Pythagorean theorem, trigonometry, sequences and series, and set theory. Construction highlights include commands like Polygon, Sequence, Length, Take, and If in GeoGebra. Suitable for high school mathematics teaching, focusing on the integration of geometric transformations and algebraic operations.

GeoGebra Commands & Parameters

  1. Polygon(Corner[1], (Corner[1] + (0.55 * Corner[2])) / 1.55, (Corner[4] + (0.55 * Corner[3])) / 1.55, Corner[4]) → poly1, b, c, d, g
  2. Sequence(m) → list1
  3. Length(list1) → a
  4. Take(list1, 2, a) → list2
  5. If(m ≟ 3, list0_1) → list3
  6. If(m ≟ 4, list0_1) → list4
  7. If(m ≟ 5, list0_2) → list5
  8. If(m ≟ 6, list0_2) → list6
  9. If(m ≟ 7, list0_3) → list7
  10. If(m ≟ 8, list0_3) → list8
  11. If(m ≟ 9, list0_3) → list9
  12. If(m ≟ 10, list0_3) → list10
  13. If(m ≟ 11, list0_4) → list11
  14. If(m ≟ 12, list0_4) → list12
  15. If(m ≟ 13, list0_5) → list13
  16. If(m ≟ 14, list0_5) → list14
  17. If(m ≟ 15, list0_5) → list15
  18. If(m ≟ 16, list0_5) → list16
  19. If(m ≟ 17, list0_6) → list17
  20. If(m ≟ 18, list0_6) → list18
  21. If(m ≟ 19, list0_7) → list19
  22. If(m ≟ 20, list0_7) → list20
  23. If(m ≟ 3, Length[list0_1]) → a1
  24. If(m ≟ 4, Length[list0_1]) → a2
  25. If(m ≟ 5, Length[list0_2]) → a3
  26. If(m ≟ 6, Length[list0_2]) → a4
  27. If(m ≟ 7, Length[list0_3]) → a5
  28. If(m ≟ 8, Length[list0_3]) → a6
  29. If(m ≟ 9, Length[list0_3]) → a7
  30. If(m ≟ 10, Length[list0_3]) → a8
  31. If(m ≟ 11, Length[list0_4]) → a9
  32. If(m ≟ 12, Length[list0_4]) → a10
  33. If(m ≟ 13, Length[list0_5]) → a11
  34. If(m ≟ 14, Length[list0_5]) → a12
  35. If(m ≟ 15, Length[list0_5]) → a13
  36. If(m ≟ 16, Length[list0_5]) → a14
  37. If(m ≟ 17, Length[list0_6]) → a15
  38. If(m ≟ 18, Length[list0_6]) → a16
  39. If(m ≟ 19, Length[list0_7]) → a17
  40. If(m ≟ 20, Length[list0_7]) → a18
  41. Sequence(i + 1, i, 101, n - 1, 1) → list21
  42. If(n ≟ 103, list1_1) → list22
  43. If(n ≟ 104, list1_1) → list23
  44. If(n ≟ 105, list1_1) → list24
  45. If(n ≟ 106, list1_1) → list25
  46. If(n ≟ 107, list1_2) → list26
  47. If(n ≟ 108, list1_2) → list27
  48. If(n ≟ 109, list1_3) → list28
  49. If(n ≟ 110, list1_3) → list29
  50. If(n ≟ 111, list1_3) → list30
  51. If(n ≟ 112, list1_3) → list31
  52. If(n ≟ 113, list1_4) → list32
  53. Length(list21) → i
  54. If(n ≟ 103, Length[list1_1]) → i1
  55. If(n ≟ 104, Length[list1_1]) → i2
  56. If(n ≟ 105, Length[list1_1]) → i3
  57. If(n ≟ 106, Length[list1_1]) → i4
  58. If(n ≟ 107, Length[list1_2]) → i5
  59. If(n ≟ 108, Length[list1_2]) → i6
  60. If(n ≟ 109, Length[list1_3]) → i7
  61. If(n ≟ 110, Length[list1_3]) → i8
  62. If(n ≟ 111, Length[list1_3]) → i9
  63. If(n ≟ 112, Length[list1_3]) → i10
  64. If(n ≟ 113, Length[list1_4]) → i11

AI Drawing Prompt Reference

This is a dynamic geometric demonstration showing the relationship between fractions and geometric transformations. The figure includes a polygon whose vertices are controlled by fractional parameters, illustrating similarity transformations. Sequences generate multiple polygons or points, lengths calculate edge lengths, and conditional statements enable dynamic updates. Overall, it visually demonstrates the connection between fractional operations and geometric transformations, suitable for mathematics education.
The prompt above was compiled from the original drawing commands and is for reference only.