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分数的加减法可视化

分数的加减法可视化
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2012-05-17 20:19
圆向量变换几何作图滑块动画
①本范例通过可视化方式演示分数的加法和减法运算过程；②涉及的核心数学概念包括分数、最小公倍数（LCM）、几何图形变换（平移、相似变换）；③作图要点：使用了GeoGebra命令如Circle（画圆）、LCM（求最小公倍数）、Sequence（数列）、Vector（向量）、Translate（平移）、GCD（最大公约数）；④适合初中及以上学生学习分数运算及几何变换，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Circle(centerR, radius) → circleR
  2. Circle(centerB, radius) → circleB
  3. LCM(denominatorR, denominatorB) → LCMdenominator
  4. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR
  5. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 360 / denominatorB, 360, 360 / denominatorB) → cutB
  6. Sequence(CircleSector[centerR, Rotate[AR, radius°, centerR], Rotate[AR, (radius + 360 / denominatorR)°, centerR]], radius, 0, 360 / denominatorR * numeratorR - 360 / denominatorR, 360 / denominatorR) → shadeR
  7. Sequence(CircleSector[centerB, Rotate[AB, (-radius - 360 / denominatorB)°, centerB], Rotate[AB, (-radius)°, centerB]], radius, 0, 360 / denominatorB * numeratorB - 360 / denominatorB, 360 / denominatorB) → shadeB
  8. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 0, 360, 360 / LCMdenominator) → cutLCMR
  9. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 0, 360, 360 / LCMdenominator) → cutLCMB
  10. Vector(centerB, A) → u
  11. Vector(centerB, B) → v
  12. Translate(circleB, Vector[showfinal * u]) → total0
  13. Translate(cutLCMB, Vector[showfinal * u]) → cuttotal0
  14. Sequence(CircleSector[centerB, Rotate[AB, (-radius - 360 / denominatorB)°, centerB], Rotate[AB, (-radius)°, centerB]], radius, 0, 360 / denominatorB * numeratorB - 360 / denominatorB, 360 / denominatorB) → E
  15. Translate(shadeB, Vector[showfinal * u]) → F
  16. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, 360 / denominatorR * numeratorR - 360 / denominatorR, 360 / denominatorR) → H
  17. Translate(H, Vector[showfinal * u]) → I
  18. Vector(centerB, J) → w
  19. Translate(circleB, Vector[showfinal * w]) → D
  20. Translate(cutLCMB, Vector[showfinal * w]) → K
  21. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, (LCMdenominator - LCMnumeratorB) * 360 / LCMdenominator, 360 / LCMdenominator * (M + LCMdenominator - LCMnumeratorB - 1), 360 / LCMdenominator) → N
  22. Translate(N, Vector[showfinal * v]) → O
  23. GCD(LCMnumerator, LCMdenominator) → P
  24. Translate(circleB, Vector[showfinal * u]) → C
  25. Translate(cutLCMB, Vector[showfinal * u]) → Q
  26. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, LCMnumeratorB * 360 / LCMdenominator, 360 / LCMdenominator * (LCMnumeratorR - 1), 360 / LCMdenominator) → R
  27. Translate(R, Vector[showfinal * u]) → S
  28. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorB)°, centerB]], radius, 0, 360 / denominatorB * numeratorB - 360 / denominatorB, 360 / denominatorB) → T
  29. Translate(circleB, Vector[showfinal * v]) → U
  30. Translate(cutLCMB, Vector[showfinal * v]) → V

AI 绘图提示语参考

画两个同心圆，用不同颜色区分。根据两个分数的分母计算最小公倍数，并以此为基础绘制多个扇形，模拟分数的几何表示。通过旋转和位移操作，将这些扇形组合，直观展示分数的加减过程。利用向量工具，将图形整体平移，对比不同分数加减后的结果，体现几何变换与分数运算的关联。
以上提示语为根据原始绘图命令整理而来，仅供参考。