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集合交集演示

集合交集演示
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2015-11-10 04:53
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所属专题 CCSS Support Math II Unit 4
①本范例演示了三个集合A、B、C的交集运算及结果的可视化；②涉及的核心数学概念包括集合交集、交集运算；③作图要点：使用了Intersection（交集）、Length（长度）、LaTeX（公式显示）等GeoGebra命令/对象；④适合高中数学学生学习和理解集合运算及三维空间中的交集概念。

GeoGebra 命令及参数

  1. Intersection(Acolour, Bcolour) → AB
  2. Intersection(Acolour, Ccolour) → AC
  3. Intersection(Bcolour, Ccolour) → BC
  4. Length(AB) → lengthAB
  5. Intersection(AB, Ccolour) → ABC
  6. Length(AC) → lengthAC
  7. Length(BC) → lengthBC
  8. Length(ABC) → lengthABC
  9. LaTeX((("\text{Set \textcolor{#000099}{A} contains the elements \textcolor{#000099}{" * Aout) * "}.}")) → text8
  10. LaTeX((("\text{Set \textcolor{#000099}{B} contains the elements \textcolor{#000099}{" * Bout) * "}.}")) → text9
  11. LaTeX((("\text{The elements that are in both Set \textcolor{#000099}{A} and Set \textcolor{#000099}{B} are \textcolor{#000099}{" * IntersectionAB) * "}.}")) → text10
  12. LaTeX((("\text{Set \textcolor{#000099}{C} contains the elements \textcolor{#000099}{" * Cout) * "}.}")) → text18
  13. LaTeX((("\text{The elements that are in both Set \textcolor{#000099}{A} and Set \textcolor{#000099}{C} are \textcolor{#000099}{" * IntersectionAC) * "}.}")) → text19
  14. LaTeX("\text{Find A∩C.}") → text6
  15. LaTeX("\text{Find B∩C.}") → text16
  16. LaTeX((("\text{Set \textcolor{#000099}{B} contains the elements \textcolor{#000099}{" * Bout) * "}.}")) → text22
  17. LaTeX((("\text{The elements that are in both Set \textcolor{#000099}{B} and Set \textcolor{#000099}{C} are \textcolor{#000099}{" * IntersectionBC) * "}.}")) → text23
  18. LaTeX("\text{Find A∩B∩C.}") → text25
  19. LaTeX("\text{To find A∩B∩C,find the elements that are in all three sets.}") → text26
  20. LaTeX((("\text{Set \textcolor{#000099}{B} contains the elements \textcolor{#000099}{" * Bout) * "}.}")) → text27
  21. LaTeX((("\text{Set \textcolor{#000099}{C} contains the elements \textcolor{#000099}{" * Cout) * "}.}")) → text28
  22. LaTeX((("\text{The elements that are in all three sets are \textcolor{#000099}{" * IntersectionABC) * "}.}")) → text29
  23. LaTeX("\text{that indicates how likely an event is to occur.}") → text13
  24. LaTeX("\text{Find A∩B.}") → text5
  25. LaTeX("\text{To find A∩B,find the elements that are in both Set \textcolor{#000099}{A} and Set \textcolor{#000099}{B}.}") → text7
  26. LaTeX("\text{To find A∩C,find the elements that are in both Set \textcolor{#000099}{A} and Set \textcolor{#000099}{C}.}") → text17
  27. LaTeX("\text{To find B∩C,find the elements that are in both Set \textcolor{#000099}{B} and Set \textcolor{#000099}{C}.}") → text21
  28. LaTeX((("\text{Number of colors in Set A=" * ValA) * "}")) → text14
  29. LaTeX((("\text{Number of colors in Set B=" * ValB) * "}")) → text15
  30. LaTeX((("\text{Number of colors in Set C=" * ValC) * "}")) → text31
  31. LaTeX("\text{Given sets A,B,and C,find A∩B,A∩C,B∩C,and A∩B∩C.}") → text1
  32. LaTeX((("\text{\mathbf{\textcolor{#000099}{A=}\left\{\textcolor{#000099}{" * Aout) * "}\right\}}}")) → text2
  33. LaTeX((("\text{\mathbf{\textcolor{#000099}{B=}\left\{\textcolor{#000099}{" * Bout) * "}\right\}}}")) → text3
  34. LaTeX((("\text{\mathbf{\textcolor{#000099}{C=}\left\{\textcolor{#000099}{" * Cout) * "}\right\}}}")) → text4
  35. LaTeX((("\text{Therefore,A∩B=\left\{\textcolor{#000099}{" * IntersectionAB) * "}\right\}.}")) → text11
  36. LaTeX((("\text{Therefore,A∩C=\left\{\textcolor{#000099}{" * IntersectionAC) * "}\right\}.}")) → text20
  37. LaTeX((("\text{Therefore,B∩C=\left\{\textcolor{#000099}{" * IntersectionBC) * "}\right\}.}")) → text24
  38. LaTeX((("\text{Therefore,A∩B∩C=\left\{\textcolor{#000099}{" * IntersectionABC) * "}\right\}.}")) → text30
  39. LaTeX("\text{\mathbf{Probability} a number from \textcolor{#000099}0 to \textcolor{#000099}1 inclusive or a percent from \textcolor{#000099}{0%} to \textcolor{#000099}{100%} inclusive}") → text12

AI 绘图提示语参考

画三个三维空间中的集合，用不同颜色表示，并展示它们的交集。首先找到两个集合的交集，用线条表示，然后找到三个集合的交集，也用线条表示。测量并标注每个交集的长度，同时用文本说明每个集合的元素和交集的结果。最终图形应包含集合、交集线条、长度标注和说明文本，清晰展示集合运算的结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。