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Venn图问题解决：用集合模型分析投票情况

Venn图问题解决：用集合模型分析投票情况
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2022-10-27 00:07
概率统计几何作图
这个范例演示了如何使用Venn图来建模和解决实际问题。核心数学概念是集合与概率，涉及如何通过Venn图计算总人数、特定电影投票数以及多选情况。作图要点包括使用GeoGebra命令如Shuffle、Element、Ellipse等来构造集合对象。适合6-8年级学生，用于培养统计与概率思维。

GeoGebra 命令及参数

  1. Shuffle(Sequence[t, t, 350, 400, 1]) → allPeople, {352, 365, 392, 355, 354, 390, 374, 381, 364, 398, 382, 351, 389, 375, 363, 400, 369, 358, 394, 361, 362, 360, 399, 356, 391, 353, 393, 379, 378, 396, 380, 386, 395, 350, 357, 377, 366, 376, 385, 388, 371, 368, 359, 387, 372, 367, 370, 373, 384, 397, 383}
  2. Shuffle(Sequence[t, t, 2, 26, 1]) → allH, {23, 6, 22, 4, 15, 18, 11, 9, 16, 5, 20, 25, 13, 26, 7, 24, 8, 21, 14, 19, 12, 2, 17, 10, 3}
  3. Shuffle(Sequence[t, t, 2, 90, 1]) → allG, {50, 79, 33, 75, 85, 26, 55, 73, 39, 60, 30, 25, 81, 52, 82, 76, 88, 83, 6, 23, 45, 11, 5, 28, 49, 61, 64, 84, 59, 43, 7, 46, 69, 51, 34, 58, 32, 9, 10, 15, 22, 13, 42, 27, 20, 62, 31, 65, 68, 48, 78, 2, 47, 90, 38, 29, 3, 12, 74, 24, 57, 18, 63, 4, 19, 37, 70, 14, 54, 41, 67, 66, 53, 89, 87, 35, 40, 56, 36, 72, 17, 8, 86, 80, 16, 44, 77, 21, 71}
  4. Shuffle(Sequence[t, t, 2, 90, 1]) → allD, {10, 72, 76, 26, 27, 50, 43, 89, 70, 36, 4, 61, 33, 71, 58, 40, 82, 69, 78, 30, 12, 53, 44, 55, 21, 31, 15, 84, 16, 18, 46, 67, 24, 41, 83, 13, 7, 74, 19, 48, 23, 20, 77, 59, 22, 37, 63, 49, 45, 80, 73, 42, 8, 39, 17, 11, 65, 38, 68, 52, 3, 57, 2, 56, 90, 81, 79, 54, 32, 62, 25, 66, 9, 75, 60, 28, 88, 29, 47, 85, 14, 34, 86, 6, 51, 64, 5, 35, 87}
  5. Shuffle(Sequence[t, t, 2, 90, 1]) → allB, {22, 18, 43, 9, 38, 33, 44, 14, 30, 47, 85, 27, 89, 68, 36, 40, 65, 67, 57, 5, 7, 20, 11, 35, 63, 28, 41, 29, 32, 3, 82, 6, 77, 78, 71, 70, 39, 42, 86, 52, 2, 61, 34, 60, 56, 64, 72, 62, 90, 81, 23, 48, 50, 84, 12, 15, 31, 76, 17, 83, 16, 4, 66, 24, 58, 51, 69, 87, 25, 13, 8, 73, 49, 10, 21, 53, 74, 75, 59, 19, 37, 80, 79, 88, 45, 46, 55, 26, 54}
  6. Shuffle(Sequence[t, t, 2, 25, 1]) → allA, {8, 17, 24, 10, 15, 7, 12, 21, 20, 25, 14, 16, 18, 9, 3, 11, 22, 23, 4, 13, 6, 2, 19, 5}
  7. Element(allA, Mod[count, Length[allA]] + 1) → a
  8. Element(allB, Mod[count, Length[allB]] + 1) → b
  9. Element(allH, Mod[count, Length[allH]] + 1) → h
  10. Element(allG, Mod[count, Length[allG]] + 1) → g
  11. Element(allD, Mod[count, Length[allD]] + 1) → d
  12. Element(allPeople, Mod[count, Length[allPeople]] + 1) → totPeople
  13. Ellipse(A, B, C) → co
  14. Vector(A, T) → v
  15. Translate(co, v) → lu
  16. Vector(A, J) → u
  17. Translate(co, u) → mo
  18. Polygon(D, E, F, G) → q1, d_1, e, f_1, g_1
  19. Ellipse(A, B, C) → coWhite
  20. Translate(co, v) → luWhite
  21. Translate(co, u) → moWhite
  22. Shuffle(Sequence[t, t, 2, 28, 1]) → allC, {5, 20, 19, 22, 2, 4, 7, 21, 13, 24, 28, 14, 9, 18, 10, 15, 17, 12, 6, 23, 11, 8, 26, 16, 27, 3, 25}
  23. Element(allC, Mod[count, Length[allC]] + 1) → c

AI 绘图提示语参考

绘制一个用于概率与集合题的维恩图布局：在平面上先确定一个中心位置，并在其周围放置一个外层椭圆轮廓作为统一集合区域；再用同心方向的平移构造出另外两个与外层椭圆同样形状的椭圆，使它们彼此相交形成三块互相重叠的区域。随后在画面中加入一组由两个顶点确定的向量方向，并沿该方向把椭圆整体平移到白色未强调的对应位置，作为对照背景。最后在下方或侧边用四边形封闭区域的方式补出一块由四个点围成的多边形，保证整体构图清晰且可用于计数或选取问题。
以上提示语为根据原始绘图命令整理而来，仅供参考。