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分数乘法演示 by Robert Fant

分数乘法演示 by Robert Fant
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2017-09-22 01:42
概率统计几何作图函数图像
①本范例通过动态演示两个分数的乘法过程，直观展示分数乘法的几何意义；②涉及核心数学概念包括分数乘法规则、几何图形（如平行四边形）的面积关系、概率与分布的基本思想；③作图要点：运用了Point, Polygon, Textfield, IndexOf, Take, Sequence, RemoveUndefined, Intersection, GCD等GeoGebra命令和对象，如mover, f2Point, f1Point, f1, f1poly等，构建分数乘法的可视化模型；④适合初中及以上数学学习者，用于理解分数乘法的本质和几何应用。

GeoGebra 命令及参数

  1. Point({1 - mover, 0}) → f2Point
  2. Point({-1 + mover, 0}) → f1Point
  3. Polygon(f1Point, f1Point + (f1, 0), f1Point + (f1, 1), f1Point + (0, 1)) → f1poly, f1point, n, p, q
  4. Polygon(f2Point, E, G, H) → poly3, f2point, e, g_1, h_1
  5. Textfield(f1Text) → InputBox1
  6. Textfield(f2Text) → InputBox2
  7. IndexOf(47, TextToUnicode[f1Text]) → slash1
  8. IndexOf(47, TextToUnicode[f2Text]) → slash2
  9. Take(f1Text, slash1 + 1) → D1Text
  10. Polygon(f1Point, f1Point + (1, 0), 4) → poly1, f, g, h, i, A, B
  11. Polygon(f2Point, f2Point + (1, 0), 4) → poly2, j, k, l, m, C, D
  12. Take(f2Text, slash2 + 1) → D2Text
  13. Sequence(Segment[f1Point + (i / D1, 0), f1Point + (i / D1, 1)], i, 1, D1 - 1) → f1Bars
  14. Sequence(Segment[f2Point + (0, i / D2), f2Point + (1, i / D2)], i, 1, D2 - 1) → f2Bars
  15. Polygon(f2Point, f2Point + (0, f2), f2Point + (1, f2), f2Point + (1, 0)) → f2poly, r, s, t, a
  16. RemoveUndefined(Sequence[If[pN / i ≟ floor(pN / i), i], i, 1, pN]) → Nfactors
  17. RemoveUndefined(Sequence[If[pD / i ≟ floor(pD / i), i], i, 1, pD]) → Dfactors
  18. Intersection(Nfactors, Dfactors) → factors
  19. GCD(N3, D3) → GCD