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同分母分数的加法与减法

同分母分数的加法与减法
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2016-02-12 15:18
向量解析几何几何作图
所属专题 Jessica's Fraction Book
①本范例演示了同分母分数的加法与减法的几何直观表示。②涉及的核心数学概念包括分数运算、最小公倍数（LCM）、几何变换（平移、旋转）和向量运算。③作图要点：使用了Circle, LCM, Sequence, Vector, Translate, GCD, Segment等GeoGebra命令和对象，如通过LCM找到共同的分母，利用Vector和Translate进行图形平移，用GCD进行几何分割。④适合初中及以上数学学习者，用于理解分数运算的几何意义和算法步骤。

GeoGebra 命令及参数

  1. Circle(centerB, radius) → circleB
  2. LCM(denominatorR, denominatorB) → LCMdenominator
  3. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR
  4. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 360 / denominatorB, 360, 360 / denominatorB) → cutB
  5. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, (-(radius°)), centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → shadeB
  6. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 0, 360, 360 / LCMdenominator) → cutLCMR
  7. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 0, 360, 360 / LCMdenominator) → cutLCMB
  8. Vector(centerB, A) → u
  9. Vector(centerB, B) → v
  10. Translate(circleB, Vector[(showfinal * u)]) → total0
  11. Translate(cutLCMB, Vector[(showfinal * u)]) → cuttotal0
  12. Translate(shadeB, Vector[(showfinal * u)]) → F
  13. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → H
  14. Translate(H, Vector[(showfinal * u)]) → I
  15. Vector(centerB, J) → w
  16. Translate(circleB, Vector[(showfinal * w)]) → D
  17. Translate(cutLCMB, Vector[(showfinal * w)]) → K
  18. 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
  19. Translate(N, Vector[(showfinal * v)]) → O
  20. GCD(LCMnumerator, LCMdenominator) → P
  21. Translate(circleB, Vector[(showfinal * u)]) → C
  22. Translate(cutLCMB, Vector[(showfinal * u)]) → Q
  23. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, (LCMnumeratorB * 360 / LCMdenominator), (360 / LCMdenominator * (LCMnumeratorR - 1)), 360 / LCMdenominator) → R
  24. Translate(R, Vector[(showfinal * u)]) → S
  25. Translate(circleB, Vector[(showfinal * v)]) → U
  26. Translate(cutLCMB, Vector[(showfinal * v)]) → V
  27. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorR)°, centerB], Rotate[AB, (-(radius°)), centerB]], radius, 0, (360 / denominatorR * numeratorB) - 360 / denominatorR, 360 / denominatorR) → E
  28. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorB) - 360 / denominatorR, 360 / denominatorR) → T
  29. Translate(N, Vector[(showfinal * v)]) → O2
  30. Translate(circleB, Vector[(showfinal * w)]) → D2
  31. Translate(circleB, Vector[(showfinal * v)]) → U2
  32. Segment(W, Z) → f
  33. Circle(centerB, radius) → circleB2
  34. Circle((0, 0), radius) → circleR3
  35. Sequence(CircleSector[(0, 0), Rotate[AR2, radius°, (0, 0)], Rotate[AR2, (radius + 360 / denominatorR)°, (0, 0)]], radius, (360 / denominatorR * Min[numeratorR, denominatorR - numeratorB]), (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → ShapeR2
  36. Sequence(Segment[(0, 0), Rotate[AR2, radius°, (0, 0)]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR2
  37. Sequence(CircleSector[centerR, Rotate[AR, radius°, centerR], Rotate[AR, (radius + 360 / denominatorR)°, centerR]], radius, 0, (360 / denominatorR * (((1 - b) * Min[denominatorR - numeratorB, numeratorR]) + (b * numeratorR))) - 360 / denominatorR, 360 / denominatorR) → shadeR
  38. Circle(centerR2, radius) → circleR2
  39. Circle(centerR2, radius) → circleR