积极 AI Logo 积极 AI

分数加减法的可视化演示

分数加减法的可视化演示
几何画板及绘图内容加载中，请稍等……
2012-10-17 13:46
圆向量数列变换几何作图
所属专题 Fracions
本范例通过两个可调节的圆形切片模型，直观展示异分母分数相加与相减时如何统一分母、合并分子并得到最终结果。涉及分数单位、通分、最小公倍数、最大公约数、向量平移、几何变换和圆面积扇形分割等概念。作图使用 Circle 构造圆，Sequence 生成扇形或刻度，Vector 与 Translate 实现切片移动和合并，LCM/GCD 计算通分分母与约分，对象包括 numeratorR、denominatorR、LCMdenominator、cutR、shadeR、shiftcircle 等，支持动态显示加减过程。适合小学高年级、初中分数运算教学、课件演示和数学可视化实验。

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

请绘制一个展示分数加减法的可调圆模型。首先，创建两个圆圈表示两个分数，每个圆圈用不同颜色区分。然后，将这些圆圈划分成若干等份，每一份代表分数的分母部分。接着，使用最小公倍数（LCM）计算出共同的分母，并将两个分数转换为具有相同分母的形式。通过向量平移和几何变换，将这些圆圈的扇区进行组合和移动，展示加减法的过程。最后，简化结果并显示最终的分数。整个构造过程包括创建圆圈、生成重复的扇区或标记、使用向量和平移来移动和组合切片以及计算最大公约数（GCD）来简化结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。