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Demonstration of Non-Random Sampling Methods

Demonstration of Non-Random Sampling Methods
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2020-03-23 10:53
FunctionProbability & StatisticsGeometric Construction
This example dynamically illustrates non-random sampling techniques and steps, involving core math concepts like statistics, step functions, trapezoids, logarithmic functions, hyperbolas, and upper/lower sums or Riemann sums. It is constructed using GeoGebra commands like Circle, Segment, Mirror, Polygon, and Vector. Suitable for high school and above students to understand statistical sampling and geometric representations of function graphs.

GeoGebra Commands & Parameters

  1. Circle((0, 5), 0.125) → c
  2. Segment((0, 5 - 0.125), (0, 4.25)) → f
  3. Segment((0, 4.5 + 0.125), (-0.125, 4.75)) → g
  4. Segment((0, 4.5 + 0.125), (0.125, 4.75)) → h
  5. Segment((0, 4.25), (-0.125, 4)) → i
  6. Segment((0, 4.25), (0.125, 4)) → j
  7. Circle((-1, 4.5), 0.125) → d
  8. Segment((-1, 4.5 - 0.125), (-1, 3.75)) → k
  9. Segment((-1, 4 + 0.125), (-1 - 0.125, 4.25)) → l
  10. Segment((-1, 4 + 0.125), (-1 + 0.125, 4.25)) → m
  11. Segment((-1, 3.75), (-1 - 0.125, 3.5)) → n
  12. Segment((-1, 3.75), (-1 + 0.125, 3.5)) → p
  13. Circle((-2, 4), 0.125) → e
  14. Circle((-1.5, 2.5), 0.125) → q
  15. Circle((-0.5, 2), 0.125) → r
  16. Circle((-2.5, 1.5), 0.125) → s
  17. Segment((-0.5, 2 - 0.125), (-0.5, 1.25)) → t
  18. Segment((-1.5, 2.5 - 0.125), (-1.5, 1.75)) → a
  19. Segment((-2, 4 - 0.125), (-2, 3.25)) → b
  20. Segment((-2.5, 1.5 - 0.125), (-2.5, 0.75)) → f_1
  21. Segment((-0.5, 1.5 + 0.125), (-0.5 - 0.125, 1.75)) → g_1
  22. Segment((-0.5, 1.5 + 0.125), (-0.5 + 0.125, 1.75)) → h_1
  23. Segment((-1.5, 2 + 0.125), (-1.5 - 0.125, 2.25)) → i_1
  24. Segment((-1.5, 2 + 0.125), (-1.5 + 0.125, 2.25)) → j_1
  25. Segment((-2, 3.5 + 0.125), (-2 - 0.125, 3.75)) → k_1
  26. Segment((-2, 3.5 + 0.125), (-2 + 0.125, 3.75)) → l_1
  27. Segment((-2.5, 1 + 0.125), (-2.5 + 0.125, 1.25)) → m_1
  28. Segment((-2.5, 1 + 0.125), (-2.5 - 0.125, 1.25)) → n_1
  29. Segment((-0.5, 1.25), (-0.5 - 0.125, 1)) → p_1
  30. Segment((-0.5, 1.25), (-0.5 + 0.125, 1)) → q_1
  31. Segment((-1.5, 1.75), (-1.5 - 0.125, 1.5)) → r_1
  32. Segment((-1.5, 1.75), (-1.5 + 0.125, 1.5)) → s_1
  33. Segment((-2, 3.25), (-2 - 0.125, 3)) → t_1
  34. Segment((-2, 3.25), (-2 + 0.125, 3)) → a_1
  35. Segment((-2.5, 0.75), (-2.5 + 0.125, 0.5)) → b_1
  36. Segment((-2.5, 0.75), (-2.5 - 0.125, 0.5)) → c_1
  37. Mirror(d, d_1) → d'
  38. Mirror(k, d_1) → k'
  39. Mirror(m, d_1) → m'
  40. Mirror(l, d_1) → l'
  41. Mirror(n, d_1) → n'
  42. Mirror(p, d_1) → p'
  43. Mirror(e, d_1) → e'
  44. Mirror(l_1, d_1) → e_1
  45. Mirror(k_1, d_1) → f_2
  46. Mirror(b, d_1) → b'
  47. Mirror(a_1, d_1) → g_2
  48. Mirror(t_1, d_1) → h_2
  49. Mirror(r, d_1) → r'
  50. Mirror(h_1, d_1) → i_2
  51. Mirror(g_1, d_1) → j_2
  52. Mirror(t, d_1) → t'
  53. Mirror(q_1, d_1) → k_2
  54. Mirror(p_1, d_1) → l_2
  55. Mirror(q, d_1) → q'
  56. Mirror(a, d_1) → a'
  57. Mirror(j_1, d_1) → m_2
  58. Mirror(i_1, d_1) → n_2
  59. Mirror(s_1, d_1) → p_2
  60. Mirror(r_1, d_1) → q_2
  61. Mirror(f_1, d_1) → r_2
  62. Mirror(s, d_1) → s'
  63. Mirror(m_1, d_1) → s_2
  64. Mirror(n_1, d_1) → t_2
  65. Mirror(c_1, d_1) → a_2
  66. Mirror(b_1, d_1) → b_2
  67. Polygon(A, B, C, D) → q1, a_3, b_3, c_2, d_2
  68. Polygon(E, F, G, H) → q2, e_2, f_3, g_3, h_3
  69. Polygon(I, J, K, L) → q3, i_3, j_3, k_3, l_3
  70. Polygon(M, N, O, P) → q4, m_3, n_3, o, p_3
  71. Vector((0.25, 4.25), (0.75, 4)) → v
  72. Polygon(Q, R, S, T) → q5, q_3, r_3, s_3, t_3
  73. Vector((-0.25, 4.25), (-0.75, 4)) → u
  74. Polygon(U, V, W, Z) → q6, u_2, v_2, w_1, z_1
  75. Polygon(A_1, B_1, C_1, D_1) → q7, a_4, b_4, c_3, d_3
  76. Polygon(E_1, F_1, G_1, H_1) → q8, e_3, f_4, g_4, h_4
  77. Polygon(I_1, J_1, K_1, L_1) → q9, i_4, j_4, k_4, l_4
  78. Vector((-1.25, 4), (-1.75, 3.5)) → w_2
  79. Vector((1.25, 4), (1.75, 3.5)) → u_3
  80. Vector((-2, 2.75), (-2.5, 1.75)) → v_3
  81. Vector((2, 2.75), (2.5, 1.75)) → w_3
  82. Vector((-0.125, 3.75 + 0.125), (-0.5, 2.25)) → w
  83. Vector((-0.25, 4), (-1.75, 3.5)) → v_1
  84. Vector((0.25, 4), (2.5, 1.75)) → u_4
  85. Vector((0.125, 3.75 + 0.125), (0.5, 2.25)) → u_1
  86. Vector((-0.75, 4), (-0.25, 4.25)) → v_4
  87. Vector((0.5, 2.25), (0.125, 3.75 + 0.125)) → w_4
  88. Vector((-0.5, 2.25), (-0.125, 3.75 + 0.125)) → c_4
  89. Vector((1.75, 3.5), (0.25, 4)) → d_4

AI Drawing Prompt Reference

Draw a figure with multiple concentric circles and segments, including 4 concentric circles each with a radius of 0.125, where each circle has a vertical segment intersecting at the center. Then, mirror these segments to another concentric circle to form a symmetrical figure. Finally, connect the endpoints of these segments to form a series of trapezoids and rectangles, illustrating non-random sampling methods.
The prompt above was compiled from the original drawing commands and is for reference only.