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蚂蚁漫步概率模拟

蚂蚁漫步概率模拟
几何画板及绘图内容加载中，请稍等……
2012-04-26 03:47
概率统计几何作图函数图像
所属专题 Statistics and Probability with Mr Downes probability
①本范例通过 GeoGebra 模拟蚂蚁在正方形内随机漫步的路径，直观展示概率统计中的随机游走现象；②涉及核心数学概念包括概率分布、随机变量、几何概率及数据收集；③作图要点运用了 Circle（圆）、RandomUniform（均匀随机数）、Segment（线段）、Distance（距离）等 GeoGebra 命令与对象构建漫步路径；④适合高中及以上学生用于理解随机过程与概率模拟，也可用于统计教学演示。

GeoGebra 命令及参数

  1. Circle(A, 3) → c
  2. RandomUniform(0, 360) → Angle
  3. RandomUniform(0, 360) → C2
  4. RandomUniform(0, 360) → C3
  5. RandomUniform(0, 360) → C4
  6. RandomUniform(0, 360) → C5
  7. RandomUniform(0, 360) → C6
  8. RandomUniform(0, 360) → C7
  9. RandomUniform(0, 360) → C8
  10. RandomUniform(0, 360) → C9
  11. RandomUniform(0, 360) → C10
  12. RandomUniform(0, 360) → C11
  13. RandomUniform(0, 360) → C12
  14. RandomUniform(0, 360) → C13
  15. RandomUniform(0, 360) → C14
  16. RandomUniform(0, 360) → C15
  17. RandomUniform(0, 360) → C16
  18. RandomUniform(0, 360) → C17
  19. RandomUniform(0, 360) → C18
  20. RandomUniform(0, 360) → C19
  21. RandomUniform(0, 360) → C20
  22. RandomUniform(0, 360) → C21
  23. Segment(A, B) → a
  24. Segment(B, C) → b
  25. Segment(C, D) → d
  26. Segment(D, E) → e
  27. Segment(F, G) → g
  28. Segment(G, H) → h
  29. Segment(H, I) → i
  30. Segment(I, J) → j
  31. Segment(J, K) → k
  32. Segment(K, L) → l
  33. Segment(L, M) → m
  34. Segment(M, N) → n
  35. Segment(N, O) → p
  36. Segment(O, P) → q
  37. Segment(P, Q) → r
  38. Segment(Q, R) → s
  39. Segment(R, S) → t
  40. Segment(S, T) → a_1
  41. Segment(T, U) → b_1
  42. Distance((A2, B2), A) → D2
  43. Distance((A3, B3), A) → D3
  44. Distance((A4, B4), A) → D4
  45. Distance((A5, B5), A) → D5
  46. Distance((A6, B6), A) → D6
  47. Distance((A7, B7), A) → D7
  48. Distance((A8, B8), A) → D8
  49. Distance((A9, B9), A) → D9
  50. Distance((A10, B10), A) → D10
  51. Distance((A11, B11), A) → D11
  52. Distance((A12, B12), A) → D12
  53. Distance((A13, B13), A) → D13
  54. Distance((A14, B14), A) → D14
  55. Distance((A15, B15), A) → D15
  56. Distance((A16, B16), A) → D16
  57. Distance((A17, B17), A) → D17
  58. Distance((A18, B18), A) → D18
  59. Distance((A19, B19), A) → D19
  60. Distance((A20, B20), A) → D20
  61. Distance((A21, B21), A) → D21
  62. RandomUniform(0, 360) → C22
  63. RandomUniform(0, 360) → C23
  64. RandomUniform(0, 360) → C24
  65. RandomUniform(0, 360) → C25
  66. RandomUniform(0, 360) → C26
  67. RandomUniform(0, 360) → C27
  68. Distance((A22, B22), A) → D22
  69. Distance((A23, B23), A) → D23
  70. Distance((A24, B24), A) → D24
  71. Distance((A25, B25), A) → D25
  72. Distance((A26, B26), A) → D26
  73. Distance((A27, B27), A) → D27
  74. Segment(U, V) → c_1
  75. Segment(V, W) → d_1
  76. Segment(Z, W) → e_1
  77. Segment(B_1, C_1) → f_1
  78. Segment(Z, A_1) → g_1
  79. Segment(A_1, B_1) → h_1
  80. Segment(E, F) → i_1

AI 绘图提示语参考

在一个正方形内，画一只蚂蚁的随机行走路径，蚂蚁从中心点出发，每次随机选择一个方向移动固定距离，用线段表示行走轨迹，并记录每次移动的角度和距离，展示概率分布和随机变量概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。