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Buffon投针实验

Buffon投针实验
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2015-12-13 19:14
圆向量概率统计几何作图
① 演示Buffon投针问题的几何概率现象，通过随机圆盘投掷估计π的近似值；② 涉及概率统计、几何概率、圆的性质、割线、中位线及向量运算等核心数学概念；③ 作图要点使用了Random、Circle、OrthogonalLine、Intersect、Line、Point、Textfield、Segment、Polygon、PolyLine、IsInRegion等GeoGebra命令，并涉及大量点、线、圆、多边形对象的动态构建；④ 适合高中概率统计单元或大学几何概率课程，帮助学生直观理解几何概率与π的关系。

GeoGebra 命令及参数

  1. Random(0, 1) → f
  2. Circle(D, 1.9 / 2) → g
  3. OrthogonalLine(D, yAxis) → h
  4. OrthogonalLine(D, xAxis) → i
  5. Intersect(g, h, 1) → G
  6. Intersect(g, i, 1) → H
  7. Line(G, i) → j
  8. Line(H, h) → k
  9. Intersect(g, h, 2) → I
  10. Intersect(g, i, 2) → J
  11. Line(I, i) → l
  12. Line(J, k) → m
  13. Intersect(k, l) → K
  14. Intersect(j, k) → L
  15. Intersect(j, m) → M
  16. Intersect(l, m) → N
  17. Intersect(xAxis, yAxis) → E
  18. Point(yAxis) → O
  19. Textfield(i_1) → CasillaDeEntrada1
  20. Segment(P, Q) → t
  21. Segment(Q, E) → a_1
  22. Point(yAxis) → R
  23. Segment(E, R) → b_1
  24. Segment(R, P) → c_1
  25. Point(c_1) → S
  26. Point(a_1) → T
  27. Segment(S, T) → d_1
  28. Point(c_1) → U
  29. Point(a_1) → V
  30. Segment(U, V) → e_1
  31. Point(c_1) → W
  32. Segment(W, F) → f_1
  33. Point(b_1) → Z
  34. Intersect(n, t, 1) → A_1
  35. Intersect(n, t, 1) → B_1
  36. Point(t) → C_1
  37. Segment(Z, C_1) → g_1
  38. Point(t) → D_1
  39. Segment(O, D_1) → h_1
  40. Polygon(F_1, B, C, E_1) → polígono1, f_2, b_2, c_2, e_2
  41. Intersect(b_1, h_1) → G_1
  42. Intersect(f_1, h_1) → H_1
  43. Intersect(a_1, f_1) → I_1
  44. Intersect(a_1, b_1) → J_1
  45. Polygon(G_1, H_1, I_1, J_1) → polígono2, g_2, h_2, i_2, j_1
  46. PolyLine(G_1, H_1, I_1, J_1, G_1) → k_1
  47. Point(k_1) → K_1
  48. Circle(K_1, 1.9 / 2) → p_1
  49. OrthogonalLine(K_1, f_1) → l_1
  50. Intersect(p_1, l_1, 2) → L_1
  51. Intersect(p_1, l_1, 1) → M_1
  52. OrthogonalLine(K_1, l_1) → m_1
  53. Intersect(p_1, m_1, 2) → N_1
  54. Intersect(p_1, m_1, 1) → O_1
  55. OrthogonalLine(N_1, m_1) → q_1
  56. OrthogonalLine(L_1, q_1) → r_1
  57. OrthogonalLine(O_1, r_1) → s_1
  58. OrthogonalLine(M_1, s_1) → t_1
  59. Intersect(s_1, t_1) → P_1
  60. Intersect(r_1, s_1) → Q_1
  61. Intersect(q_1, r_1) → R_1
  62. Intersect(q_1, t_1) → S_1
  63. Textfield(n_1) → CasillaDeEntrada2
  64. Textfield(n) → CasillaDeEntrada3
  65. IsInRegion(D, a(x, y) ∨ c(x, y) ∨ d(x, y) ∨ e(x, y) ∨ o(x, y) ∨ q(x, y) ∨ p(x, y) ∨ r(x, y) ∨ s(x, y) ∨ o_1(x, y) ∨ u_1(x, y) ∨ v_1(x, y)) → b