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弹珠袋模拟

弹珠袋模拟
几何画板及绘图内容加载中，请稍等……
2013-06-07 12:33
函数概率统计几何作图
所属专题 Statistics Demonstrations Statistics Demonstrations Statistics Demonstrations Statistics Demonstrations Statistics Demonstrations
①本范例演示了从装有不同颜色弹珠的袋中随机抽取弹珠（可重复抽取）的过程，并通过条形图展示抽取结果的概率分布；②涉及的核心数学概念包括概率统计、百分比、比例、函数图像等；③作图要点——从下方『构造摘要』提炼用到了If, Circle, Sequence, CountIf, Vector, Element, Polygon, Midpoint, Line等GeoGebra命令/对象；④适合高中阶段学习概率统计、数据分析的学生使用。

GeoGebra 命令及参数

  1. If(N_{colors} < -1, R, 0) → R2
  2. If(N_{colors} < -1 * 2, G, 0) → G2
  3. If(N_{colors} < -1 * 3, P, 0) → P2
  4. If(N_{colors} < 0, B, 0) → B2
  5. If(rand_{bag-blue} > 0.5, -1, 1) → posneg_{blue}
  6. If(rand_{bag-red} > 0.5, 1, -1) → posneg_{red}
  7. Circle(Drawn_{marble-center}, 0.3) → MarbleDrawnCircleRed
  8. Circle(Drawn_{marble-center}, 0.3) → MarbleDrawnCircleGreen
  9. Circle(Drawn_{marble-center}, 0.3) → MarbleDrawnCircleBlue
  10. Circle(Drawn_{marble-center}, 0.3) → f
  11. Sequence((x(Marble_{bag-center}) + i * posneg_{red} * 0.05 * random(), y(Marble_{bag-center}) + 0.15 + 0.4 * random()), i, -8, R2 - 9) → Add_{marbles-to-bag-red}
  12. If(rand_{bag-green} > 0.5, -1, 1) → posneg_{green}
  13. Sequence((x(Marble_{bag-center}) + i * posneg_{green} * 0.05 * random(), y(Marble_{bag-center}) + 0.2 + 0.4 * random()), i, -8, G2 - 9) → Add_{marbles-to-bag-green}
  14. If(rand_{bag-purple} < 0.5, 1, -1) → posneg_{purple}
  15. Sequence((x(Marble_{bag-center}) + i * posneg_{purple} * 0.05 * random(), y(Marble_{bag-center}) + 0.25 + 0.5 * random()), i, -8, P2 - 9) → Add_{marbles-bag-purple}
  16. Sequence(ceil((random() + a - a) * (B + R2 + G2 + P2)) + i - i, i, 1, a) → List_{colors}
  17. CountIf(x ≤ B, List_{colors}) → Count_{blue}
  18. CountIf(B < x ≤ B + R2, List_{colors}) → Count_{red}
  19. CountIf(B + R2 < x ≤ B + R2 + G2, List_{colors}) → Count_{green}
  20. CountIf(B + R2 + G2 < x ≤ B + R2 + G2 + P2, List_{colors}) → Count_{purple}
  21. Circle((x(Marble_{bag-center}), y(Marble_{bag-center})), 0.03) → Marble_{blue}
  22. Vector(Marble_{bag-center}, D) → v
  23. Element(List_{colors}, a) → MarbleDrawnValue
  24. Sequence((x(Marble_{bag-center}) + i * posneg_{blue} * 0.05 * random(), y(Marble_{bag-center}) + 0.1 + 0.4 * random()), i, -8, B2 - 9) → Add_{marbles-to-bag-blue}
  25. Polygon(BlueBarBottomLeft, BlueBarBottomRt, BlueBarTopRt, BlueBarTopLeft) → BlueBar, a_1, c_1, e_1, f_1
  26. Polygon(RedBarBottomLeft, RedBarBottomRt, RedBarTopRt, RedBarTopLeft) → RedBar, a_2, c_2, e_2, f_2
  27. Midpoint(BlueBarTopLeft, BlueBarTopRt) → BlueBarTopMidpoint
  28. Polygon(GreenBarBottomLeft, GreenBarBottomRt, GreenBarTopRt, GreenBarTopLeft) → GreenBar, a_3, c, e, f_3
  29. Polygon(PurpleBarBottomLeft, PurpleBarBottomRt, PurpleBarTopRt, PurpleBarTopLeft) → PurpleBar, h, i, j, k
  30. Midpoint(RedBarTopLeft, RedBarTopRt) → RedBarTopMidpt
  31. Midpoint(GreenBarTopLeft, GreenBarTopRt) → GreenBarTopMidpt
  32. Midpoint(PurpleBarTopLeft, PurpleBarTopRt) → PurpleBarTopMidpt
  33. Line(DividerLeft, DividerRight) → l

AI 绘图提示语参考

在一个袋子里随机抽取不同颜色的弹珠，展示抽取结果的概率分布。用条形图表示不同颜色弹珠的数量，并在袋子上绘制弹珠。先画出袋子和中心点，再随机生成红色、绿色、紫色弹珠并放置在袋子上。接着模拟抽取过程，在中心点绘制抽取的弹珠，并用条形图显示各颜色弹珠的数量分布。
以上提示语为根据原始绘图命令整理而来，仅供参考。