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分数加法可视化 by mathspace

分数加法可视化 by mathspace
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2013-10-04 14:09
圆向量解析几何最值优化
所属专题 Fracions
①本范例通过动态演示，直观展示分数加法中寻找和运用最小公倍数（LCM）来统一分母的过程；②涉及的核心数学概念包括：分数加法、最小公倍数（LCM）、最大公约数（GCD）、向量、几何变换等；③作图要点：利用GeoGebra命令如Circle（画圆）、LCM（求最小公倍数）、Vector（向量）、Translate（平移）、GCD（求最大公约数）等，构建分数的分子分母、统一分母后的图形表示，并实现动态交互；④适合初中及以上数学学习者，用于理解分数加法原理及几何直观。

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