韦恩图绘制 by Steve Phelps

韦恩图绘制 by Steve Phelps
几何画板及绘图内容加载中,请稍等……
2017-01-01 05:42
①本范例演示如何使用 GeoGebra 绘制韦恩图;②涉及核心数学概念包括集合运算、逻辑关系、解析几何;③作图要点:使用 Point, Circle, Intersect, Integral, IntegralBetween, Polygon, PolyLine, LaTeX, Random 等命令和对象;④适合高中及以上学生学习和理解集合论及几何作图。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, 2) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, 2) → d
  5. Intersect(c, d, 2) → C
  6. Circle(C, 2) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(c, e, 2) → F
  10. Intersect(c, xAxis, 1) → G
  11. Intersect(d, xAxis, 2) → H
  12. Integral(h, -3, -1) → a
  13. IntegralBetween(h, g, -1, 0) → b
  14. Integral(hh, -3, -2) → i
  15. Integral(p, -2, -1) → j
  16. IntegralBetween(g, p, -1, 0) → k
  17. IntegralBetween(h, p, 0, 1) → l
  18. IntegralBetween(g, h, 0, 1) → m
  19. Integral(g, 1, 3) → n
  20. Integral(gg, 2, 3) → o
  21. Integral(p, 1, 2) → q
  22. IntegralBetween(hh, pp, -2, 0) → r
  23. IntegralBetween(gg, pp, 0, 2) → s
  24. IntegralBetween(p, hh, -2, -1) → t
  25. IntegralBetween(gg, hh, -1, 0) → u
  26. IntegralBetween(hh, gg, 0, 1) → v
  27. IntegralBetween(p, gg, 1, 2) → w
  28. Integral(p, -1, 1) → a_1
  29. Integral(gg, -1, 0) → b_1
  30. Polygon((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5)) → poly1, f_1, g_1, h_1, i_1
  31. PolyLine((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5), (-4.5, 2.5)) → j_1
  32. Integral(hh, 0, 1) → ccc
  33. LaTeX("A \cap \left( B' \cup C' \right)") → B1
  34. LaTeX("A \cap C' ") → B2
  35. LaTeX("\left(A \cup B \right) \cap C' ") → B3
  36. LaTeX("A") → B4
  37. LaTeX("A \cap B") → B5
  38. LaTeX("A \cap B \cap C") → B6
  39. LaTeX("A \cap C") → B8
  40. LaTeX("B \cap C") → B9
  41. LaTeX("B \cap \left( A' \cup C' \right)") → B10
  42. LaTeX("C \cap \left( A' \cup B' \right)") → B11
  43. LaTeX("A \cap B \cap C'") → B12
  44. LaTeX("A \cap B' \cap C") → B13
  45. LaTeX("A' \cap B \cap C") → B14
  46. LaTeX("\left( B \cup C \right)' ") → B15
  47. LaTeX("\left( A \cup C \right)' ") → B16
  48. LaTeX("\left( A \cup B \right)' ") → B17
  49. LaTeX("A' ") → B18
  50. LaTeX("B' ") → B19
  51. LaTeX("C' ") → B20
  52. LaTeX("\left(B \cup C \right) \cap A' ") → B21
  53. LaTeX("\left(A \cup C \right) \cap B' ") → B22
  54. LaTeX("\left( A \cup B \cup C \right)' ") → B7
  55. Random(1, 22) → pick

AI 绘图提示语参考

画一个包含两个相交圆的维恩图,展示集合的交集和并集关系。首先绘制两个半径为2的圆,使它们在x轴上相交。接着,在圆内和圆外添加多个点,并用线条连接这些点,形成封闭的多边形区域。最后,在图的周围添加LaTeX公式,标注不同的集合运算结果,如A∩B、A∪B等。
以上提示语为根据原始绘图命令整理而来,仅供参考。