积极 AI Logo 积极 AI

异分母分数的加减法

异分母分数的加减法
几何画板及绘图内容加载中，请稍等……
2015-08-06 04:22
数列解析几何
本范例演示了异分母分数的加减法过程。核心数学概念包括分数、最小公倍数和通分。通过使用GeoGebra命令如Circle、LCM、Sequence等，可以直观地展示分数加减法的几何意义。适合小学高年级和初中学生学习。

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，分别用不同颜色表示，并在每个圆内用线条分割成若干扇形，扇形数量与圆的半径成反比。接着，计算两个圆的半径的最小公倍数，并以此为基础绘制新的同心圆和扇形，展示分数加减的几何意义。最后，将其中一个圆的扇形按照最小公倍数的比例移动，并与另一个圆的扇形叠加，形成新的图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。