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分数加减法作图示例

分数加减法作图示例
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2015-08-11 00:31
圆数列几何作图
本范例演示如何通过GeoGebra绘制分数加减法的图形。核心数学概念包括分数运算、公分母与最小公倍数。作图要点涉及使用Circle、LCM、Sequence等命令构建图形。适合初中生学习分数运算及几何作图。

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

绘制两个等半径的圆，分别代表两个分数。每个圆按各自分母等分，并用扇形着色表示分子部分。接着，以两个分母的最小公倍数为新的等分数，重新分割两个圆，展示通分过程。将第二个圆平移复制到第一个圆旁，并将两个着色扇形合并，直观展示分数相加的结果。再复制一个圆，平移至下方，用不同颜色表示分数相减的差。所有分割线、着色区域和移动后的图形需清晰对应，体现分数运算的几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。