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骰子投掷模拟

骰子投掷模拟
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2018-10-23 04:23
立体几何概率统计几何作图
①本范例演示了六面骰子的投掷过程及其概率分布；②涉及的核心数学概念包括概率统计、几何变换和立体几何；③作图要点——从下方『构造摘要』提炼用到了Point（点）、Cube（立方体）、Circle（圆）、Line（直线）、Rotate（旋转）等GeoGebra命令和对象；④适合高中阶段学生学习概率统计与立体几何知识，也可用于数学建模教学。

GeoGebra 命令及参数

  1. Point(Circle[(0, 0, 1), Distance[(0, 0, 0), (0, 0, 1)], Segment[(0, 0, 0), (0, 0, 1)]]) → A
  2. Cube((0, 0, 0), (0, 0, 1), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. Circle((0.5, -0.01, 0.5), p, yAxis) → c
  4. Circle((1.01, 0.5 + s, 0.5 - s), p, xAxis) → c_1
  5. Circle((1.01, 0.5 - s, 0.5 - s), p, xAxis) → d_1
  6. Circle((d, 1.01, 3 / 6), p, yAxis) → e
  7. Circle((1.01, 0.5 - s, 0.5 + s), p, xAxis) → e_1
  8. Circle((d, 1.01, 0.5 - s), p, yAxis) → f
  9. Circle((-0.01, 0.5 - s, 0.5 + s), p, xAxis) → f_1
  10. Circle((d, 1.01, 0.5 + s), p, yAxis) → g
  11. Circle((-0.01, 0.5 + s, 0.5 - s), p, xAxis) → g_1
  12. Circle((1 - d, 1.01, 0.5), p, yAxis) → h
  13. Circle((1 - d, 1.01, 0.5 + s), p, yAxis) → k
  14. Circle((0.5 + s, 0.5 + s, -0.01), p, zAxis) → k_1
  15. Circle((0.5 - s, 0.5 - s, -0.01), p, zAxis) → p_1
  16. Circle((1 - d, 1.01, 0.5 - s), p, yAxis) → q
  17. Circle((0.5 - s, 0.5 - s, 1.01), p, zAxis) → q_1
  18. Circle((1.01, 0.5, 0.5), p, xAxis) → r
  19. Circle((0.5 - s, 0.5 + s, 1.01), p, zAxis) → r_1
  20. Circle((0.5 + s, 0.5 + s, 1.01), p, zAxis) → s_1
  21. Circle((1.01, 0.5 + s, 0.5 + s), p, xAxis) → t
  22. Circle((0.5 + s, 0.5 - s, 1.01), p, zAxis) → t_1
  23. Circle((0.5, 0.5, -0.01), p, zAxis) → h_1
  24. Line(M, yAxis) → i
  25. Line(M, xAxis) → j
  26. Line(M, zAxis) → l
  27. Rotate(Rotate[Rotate[a, α, i], β, j], γ, l) → b
  28. Rotate(Rotate[Rotate[c, α, i], β, j], γ, l) → c_2
  29. Rotate(Rotate[Rotate[c_1, α, i], β, j], γ, l) → d_2
  30. Rotate(Rotate[Rotate[d_1, α, i], β, j], γ, l) → e_2
  31. Rotate(Rotate[Rotate[e, α, i], β, j], γ, l) → f_2
  32. Rotate(Rotate[Rotate[e_1, α, i], β, j], γ, l) → g_2
  33. Rotate(Rotate[Rotate[f, α, i], β, j], γ, l) → h_2
  34. Rotate(Rotate[Rotate[f_1, α, i], β, j], γ, l) → k_2
  35. Rotate(Rotate[Rotate[g, α, i], β, j], γ, l) → p_2
  36. Rotate(Rotate[Rotate[g_1, α, i], β, j], γ, l) → q_2
  37. Rotate(Rotate[Rotate[h, α, i], β, j], γ, l) → r_2
  38. Rotate(Rotate[Rotate[h_1, α, i], β, j], γ, l) → s_2
  39. Rotate(Rotate[Rotate[k, α, i], β, j], γ, l) → t_2
  40. Rotate(Rotate[Rotate[k_1, α, i], β, j], γ, l) → c_3
  41. Rotate(Rotate[Rotate[p_1, α, i], β, j], γ, l) → d_3
  42. Rotate(Rotate[Rotate[q, α, i], β, j], γ, l) → e_3
  43. Rotate(Rotate[Rotate[q_1, α, i], β, j], γ, l) → f_3
  44. Rotate(Rotate[Rotate[r, α, i], β, j], γ, l) → g_3
  45. Rotate(Rotate[Rotate[r_1, α, i], β, j], γ, l) → h_3
  46. Rotate(Rotate[Rotate[s_1, α, i], β, j], γ, l) → k_3
  47. Rotate(Rotate[Rotate[t, α, i], β, j], γ, l) → p_3
  48. Rotate(Rotate[Rotate[t_1, α, i], β, j], γ, l) → q_3