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埃及分数演示

埃及分数演示
几何画板及绘图内容加载中，请稍等……
2018-05-08 21:59
数列概率统计几何作图
①本范例演示如何将一个分数拆分为埃及分数（即分子为1的分数之和）；②涉及核心数学概念包括分数、序列、几何图形绘制、条件概率；③构造中使用了Random, Polygon, Zip, Append, Sequence, FractionText, Flatten, Textfield等GeoGebra命令和对象；④适合初中及以上数学学习者，用于理解分数拆分和序列生成。

GeoGebra 命令及参数

  1. Random(3, 12) → D
  2. Random(2, D - 1) → N
  3. Polygon((0, 0), (fraction, 0), (fraction, 0.1), (0, 0.1)) → drawnFraction, f, g, h, i
  4. Polygon((Sum[added], 0.11), (Sum[added] + 1 / availableDenoms(n), 0.11), (Sum[added] + 1 / availableDenoms(n), 0.21), (Sum[added], 0.21)) → liveFraction, j, k, l, m
  5. Zip(FractionText[AAA], AAA, Last[added, Length[added] - 1]) → displayTextHelper
  6. Append(0, Zip[1 / AAA, AAA, Last[greedyList, Length[greedyList] - 1]]) → greedyListAsFractions
  7. Sequence(Polygon[(Sum[greedyListAsFractions, i], -0.11), (Sum[greedyListAsFractions, i + 1], -0.11), (Sum[greedyListAsFractions, i + 1], -0.01), (Sum[greedyListAsFractions, i], -0.01)], i, 1, Length[greedyListAsFractions] - 1) → drawnGreedyFractions
  8. Sequence(Polygon[(Sum[added, i], 0.11), (Sum[added, i + 1], 0.11), (Sum[added, i + 1], 0.21), (Sum[added, i], 0.21)], i, 1, Length[added] - 1) → drawnAddedFractions
  9. Polygon((0, 0), (1, 0), (1, 0.1), (0, 0.1)) → origWhole, p, q, r, s
  10. Polygon((0, -0.11), (1, -0.11), (1, -0.01), (0, -0.01)) → greedyWhole, t, a, b, c
  11. Polygon((0, 0.11), (1, 0.11), (1, 0.21), (0, 0.21)) → addedWhole, d, e, f_1, g_1
  12. FractionText(fraction) → text2
  13. Flatten(Sequence[displayTextHelper(i) + "+", i, 1, Length[displayTextHelper]]) → noAnswerYet
  14. Sequence(Text[(("$\frac{1}{" * Element[usedDenoms, i]) * "}$")], i, 1, Length[usedDenoms]) → L_1
  15. Textfield(typedText) → InputBox1
  16. Zip(FractionText[1 / AAA], AAA, Last[greedyList, Length[greedyList] - 1]) → greedyDisplayHelper