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分数的意义：整体与部分的可视化模型

分数的意义：整体与部分的可视化模型
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2019-06-11 03:15
圆数列几何作图滑块动画
所属专题 Fraction Book
本范例通过多种几何模型直观展示分数的含义，即整体被等分后各部分与整体的关系。核心数学概念是分数的基本定义、等分、部分与整体的比例关系，以及分数与几何图形的对应。作图要点包括：使用Circle命令绘制圆形作为整体，通过OrthogonalLine和Intersect构造等分线，利用Sequence和Element生成多个扇形楔块（Wedge），并用Segment连接关键点；对象如NumberOfParts控制等分数，WedgeSize和WedgeDots调整显示细节，多个Wedge对象（Wedge01至Wedge20）表示不同等分部分，colorchanger系列用于动态着色。该范例适合小学高年级至初中阶段的学生学习分数概念，也可用于教师课堂演示，帮助学生从视觉上理解分子分母的意义。

GeoGebra 命令及参数

  1. Circle(A, radius) → c
  2. OrthogonalLine(A, xAxis) → f
  3. Intersect(c, f, 2) → B
  4. Sequence(Rotate[B, (WedgeSize° * i), A], i, 0, NumberOfParts) → WedgeDots
  5. Sequence(CircleSector[A, Element[WedgeDots, i], Element[WedgeDots, i + 1]], i, 1, NumberOfParts) → Wedges
  6. Element(Wedges, 1) → Wedge01
  7. Element(Wedges, 2) → Wedge02
  8. Element(Wedges, 3) → Wedge03
  9. Element(Wedges, 4) → Wedge04
  10. Element(Wedges, 5) → Wedge05
  11. Element(Wedges, 6) → Wedge06
  12. Element(Wedges, 7) → Wedge07
  13. Element(Wedges, 8) → Wedge08
  14. Element(Wedges, 9) → Wedge09
  15. Element(Wedges, 10) → Wedge10
  16. Element(Wedges, 11) → Wedge11
  17. Element(Wedges, 12) → Wedge12
  18. Element(Wedges, 13) → Wedge13
  19. Element(Wedges, 14) → Wedge14
  20. Element(Wedges, 15) → Wedge15
  21. Element(Wedges, 16) → Wedge16
  22. Element(Wedges, 17) → Wedge17
  23. Element(Wedges, 18) → Wedge18
  24. Element(Wedges, 19) → Wedge19
  25. Element(Wedges, 20) → Wedge20
  26. Segment(C, D) → g
  27. Segment(D, E) → h
  28. Segment(E, F) → i
  29. Segment(F, C) → j
  30. Sequence(C + ((StripWidth * i), 0), i, 0, NumberOfParts) → LowerDots
  31. Sequence(F + ((StripWidth * i), 0), i, 0, NumberOfParts) → UpperDots
  32. Sequence(Polygon[Element[LowerDots, i], Element[LowerDots, i + 1], Element[UpperDots, i + 1], Element[UpperDots, i]], i, 1, NumberOfParts) → VerticalStripsList
  33. Element(VerticalStripsList, 1) → Vertical01
  34. Element(VerticalStripsList, 2) → Vertical02
  35. Element(VerticalStripsList, 3) → Vertical03
  36. Element(VerticalStripsList, 4) → Vertical04
  37. Element(VerticalStripsList, 5) → Vertical05
  38. Element(VerticalStripsList, 6) → Vertical06
  39. Element(VerticalStripsList, 7) → Vertical07
  40. Element(VerticalStripsList, 8) → Vertical08
  41. Element(VerticalStripsList, 9) → Vertical09
  42. Element(VerticalStripsList, 10) → Vertical10
  43. Element(VerticalStripsList, 11) → Vertical11
  44. Element(VerticalStripsList, 12) → Vertical12
  45. Element(VerticalStripsList, 13) → Vertical13
  46. Element(VerticalStripsList, 14) → Vertical14
  47. Element(VerticalStripsList, 15) → Vertical15
  48. Element(VerticalStripsList, 16) → Vertical16
  49. Element(VerticalStripsList, 17) → Vertical17
  50. Element(VerticalStripsList, 18) → Vertical18
  51. Element(VerticalStripsList, 19) → Vertical19
  52. Element(VerticalStripsList, 20) → Vertical20
  53. Segment(G, H) → k
  54. Segment(H, I) → l
  55. Segment(I, J) → m
  56. Segment(J, G) → n
  57. Sequence(G + (0, (StripWidth * i)), i, 0, NumberOfParts) → LeftDots
  58. Sequence(H + (0, (StripWidth * i)), i, 0, NumberOfParts) → RightDots
  59. Sequence(Polygon[Element[LeftDots, i], Element[RightDots, i], Element[RightDots, i + 1], Element[LeftDots, i + 1]], i, 1, NumberOfParts) → HorizontalStripsList
  60. Element(HorizontalStripsList, 1) → Horizontal01
  61. Element(HorizontalStripsList, 2) → Horizontal02
  62. Element(HorizontalStripsList, 3) → Horizontal03
  63. Element(HorizontalStripsList, 4) → Horizontal04
  64. Element(HorizontalStripsList, 5) → Horizontal05
  65. Element(HorizontalStripsList, 6) → Horizontal06
  66. Element(HorizontalStripsList, 7) → Horizontal07
  67. Element(HorizontalStripsList, 8) → Horizontal08
  68. Element(HorizontalStripsList, 9) → Horizontal09
  69. Element(HorizontalStripsList, 10) → Horizontal10
  70. Element(HorizontalStripsList, 11) → Horizontal11
  71. Element(HorizontalStripsList, 12) → Horizontal12
  72. Element(HorizontalStripsList, 13) → Horizontal13
  73. Element(HorizontalStripsList, 14) → Horizontal14
  74. Element(HorizontalStripsList, 15) → Horizontal15
  75. Element(HorizontalStripsList, 16) → Horizontal16
  76. Element(HorizontalStripsList, 17) → Horizontal17
  77. Element(HorizontalStripsList, 18) → Horizontal18
  78. Element(HorizontalStripsList, 19) → Horizontal19
  79. Element(HorizontalStripsList, 20) → Horizontal20

AI 绘图提示语参考

画一个圆形代表整体，从圆心向水平线作垂线，交点将圆分成若干等份，用扇形表示每个分数部分，并用不同颜色区分，同时用矩形条展示每个部分与整体的关系，通过滑块控制份数，展示分数的几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。