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Ant Walk Probability Simulation

Ant Walk Probability Simulation
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2012-04-26 03:47
Probability & StatisticsGeometric ConstructionGraphing
In collections Statistics and Probability with Mr Downes probability
This example demonstrates a 2D probability question involving random walks using GeoGebra. It visualizes and collects data on an ant's random path within a square, highlighting concepts like probability distributions, random variables, geometric probability, and data analysis. Constructed using commands like Circle, RandomUniform, Segment, and Distance, it is suitable for high school and above to explore stochastic processes and probability simulations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Visualize an ant's random walk within a square, starting from the center. Each step is randomly chosen in direction and fixed length, represented by line segments. Record the angle and distance of each move to illustrate probability distributions and random variables.
The prompt above was compiled from the original drawing commands and is for reference only.