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分数乘法 GeoGebra 示例

分数乘法 GeoGebra 示例
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2019-10-04 16:00
多边形向量几何作图
①本范例演示分数乘法的几何表示与计算过程；②涉及核心数学概念包括分数运算、几何图形变换、向量与多边形；③构造要点：使用 Point, Polygon, Textfield, IndexOf, Take, Sequence, RemoveUndefined, Intersection 等命令创建图形与交互元素；④适合初中及以上数学教学，用于理解分数乘法的直观意义和应用。

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