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Animation 204: Composite Demonstration of Geometric Transformations and Probabil

Animation 204: Composite Demonstration of Geometric Transformations and Probabil
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2017-02-21 12:38
多边形概率统计变换几何作图滑块动画
This GeoGebra example presents a composite animation that integrates geometric constructions with probability statistics, featuring shapes such as squares, rhombi, circles, sectors, and polygons, along with concepts like binomial distribution, special points, and equations. The construction employs commands including Circle, Point, Polygon, Dilate, Segment, Rotate, Min, Intersect, CircleSector, Vector, Translate, Line, Angle, Midpoint, and OrthogonalLine, creating numerous points, segments, polygons, and transformed objects, with dynamic changes driven by sliders or animation. It is suitable for high school and above to explore the visual connection between geometric transformations (rotation, translation, scaling) and probability distributions (binomial), and can serve as a teaching tool for demonstrating the combination of dynamic geometry and statistical simulation.

GeoGebra 命令及参数

  1. Circle(A, b) → d
  2. Point(d) → B
  3. Circle(B, c) → e
  4. Point(e) → C
  5. Polygon(A, B, 4) → poly1, f, g, h, i, D, E
  6. Polygon(C, B, 4) → poly2, j, k, l, m, F, G
  7. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], A) → B'
  8. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], F) → B'_1
  9. Segment(B, B') → n
  10. Segment(B, B'_1) → p
  11. Rotate(B, If[1 < a ≤ 2, ((-(a - 1)) * π / 2), ((-π)) / 2], F) → B'_2
  12. Rotate(B'_1, If[1 < a ≤ 2, ((-(a - 1)) * π / 2), ((-π)) / 2], F) → L
  13. Segment(B'_2, L) → p'
  14. Rotate(B, If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], A) → B'_3
  15. Rotate(B', If[1 < a ≤ 2, ((a - 1) * π / 2), π / 2], A) → B''
  16. Segment(B'_3, B'') → n'
  17. Rotate(B'_2, If[2 < a ≤ 3, ((-(a - 2)) * π / 2), ((-π)) / 2], G) → M
  18. Rotate(L, If[2 < a ≤ 3, ((-(a - 2)) * π / 2), ((-π)) / 2], G) → L'
  19. Segment(M, L') → p''
  20. Rotate(B'_3, If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], E) → N
  21. Rotate(B'', If[2 < a ≤ 3, ((a - 2) * π / 2), π / 2], E) → B'''
  22. Segment(N, B''') → n''
  23. Rotate(N, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], D) → N'
  24. Rotate(B''', If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], D) → O
  25. Segment(N', O) → n'''
  26. Rotate(M, If[3 < a ≤ 4, ((-(a - 3)) * π / 2), ((-π)) / 2], C) → M'
  27. Rotate(L', If[3 < a ≤ 4, ((-(a - 3)) * π / 2), ((-π)) / 2], C) → L''
  28. Segment(M', L'') → p'''
  29. Segment(F, G) → q
  30. Segment(F, B) → r
  31. Segment(A, B) → s
  32. Min(r, s) → o
  33. Circle(F, (0.15 * o)) → t
  34. Intersect(l, q) → P
  35. Intersect(t, q) → Q,
  36. Intersect(t, r) → R,
  37. CircleSector(F, Q, R) → c_1
  38. Dilate(F, If[4 < a ≤ 5, 5 - a, 0], C) → F'
  39. Vector(F, F') → u
  40. Translate(c_1, u) → d_1
  41. Rotate(d_1, If[5 < a ≤ 6, ((a - 5) * π), π], C) → e_1
  42. Dilate(F, If[6 < a ≤ 7, 7 - a, 0], A) → F'_1
  43. Dilate(C, If[6 < a ≤ 7, 7 - a, 0], E) → C'
  44. Vector(F, F'_1) → v
  45. Vector(C, C') → w
  46. Translate(e_1, w) → f_1
  47. Translate(c_1, v) → g_1
  48. Line(A, p) → h_1
  49. Line(E, p''') → i_1
  50. Point(h_1) → S
  51. Angle(S, A, E) → α
  52. Rotate(g_1, If[7 < a ≤ 8, ((-(a - 7)) * ((2 * π) - α)), (-((2 * π) - α))], A) → k_1
  53. Line(E, h_1) → j_1
  54. Point(j_1) → T
  55. Angle(D, E, T) → β
  56. Rotate(f_1, If[7 < a ≤ 8, ((-(a - 7)) * β), (-β)], E) → p_1
  57. Dilate(E, If[8 < a ≤ 9, 9 - a, 0], G) → E'
  58. Dilate(F, If[8 < a ≤ 9, 9 - a, 0], D) → F'_2
  59. Vector(E, E') → u_1
  60. Vector(F, F'_2) → v_1
  61. Translate(p_1, u_1) → q_1
  62. Translate(c_1, v_1) → r_1
  63. Line(G, n'') → l_1
  64. Point(l_1) → U
  65. Line(G, n') → m_1
  66. Point(m_1) → V
  67. Angle(C, G, V) → γ
  68. Rotate(q_1, If[8 < a ≤ 9, ((-(a - 8)) * γ), (-γ)], E') → s_1
  69. Line(D, p) → n_1
  70. Point(n_1) → W
  71. Angle(W, D, B) → δ
  72. Rotate(r_1, If[8 < a ≤ 9, ((a - 8) * δ), δ], F'_2) → t_1
  73. Midpoint(A, B) → Z
  74. Midpoint(B, C) → A_1
  75. Midpoint(Z, B) → B_1
  76. Midpoint(A_1, B) → C_1
  77. Dilate(C, If[9 < a ≤ 10, 10 - a, 0], C_1) → C'_1
  78. Dilate(A, If[9 < a ≤ 10, 10 - a, 0], B_1) → A'
  79. Vector(A, A') → w_1
  80. Vector(C, C'_1) → a_1
  81. Translate(e_1, a_1) → c_2
  82. Translate(k_1, w_1) → d_2
  83. Rotate(d_2, If[10 < a ≤ 11, ((a - 10) * π / 2), π / 2], B_1) → e_2
  84. Rotate(c_2, If[10 < a ≤ 11, ((a - 10) * π / 2), π / 2], C_1) → f_2
  85. Dilate(C_1, If[11 < a ≤ 12, 12 - a, 0], B) → D_1
  86. Dilate(B_1, If[11 < a ≤ 12, 12 - a, 0], B) → E_1
  87. Vector(B_1, E_1) → b_1
  88. Vector(C_1, D_1) → u_2
  89. Translate(e_2, b_1) → g_2
  90. Translate(f_2, u_2) → h_2
  91. Segment(D, C) → a_3
  92. Segment(A, F) → b_3
  93. Line(A, B) → f_4
  94. Polygon(A, F, B) → poly4, b_4, a_4, f_5
  95. Polygon(B, C, D) → poly5, d_4, b_5, c_4
  96. OrthogonalLine(F, f_4) → h_4
  97. Line(D, B) → g_4
  98. OrthogonalLine(C, g_4) → i_4
  99. Intersect(f_4, h_4) → R_1
  100. Intersect(g_4, i_4) → S_1
  101. Dilate(B, If[13 < a ≤ 14, 14 - a, 0], R_1) → B'_4
  102. Dilate(F, If[13 < a ≤ 14, 14 - a, 0], R_1) → F'_3
  103. Angle(B, R_1, F) → ε
  104. Segment(B, B'_4) → i_2
  105. Segment(F, F'_3) → j_2
  106. Dilate(A, If[12 < a ≤ 13, 13 - a, 0], F) → A'_1
  107. Dilate(D, If[12 < a ≤ 13, 13 - a, 0], C) → D'
  108. Segment(D, D') → k_2
  109. Segment(A, A'_1) → l_2
  110. Dilate(C, If[14 < a ≤ 15, 15 - a, 0], S_1) → C'_2
  111. Dilate(D, If[14 < a ≤ 15, 15 - a, 0], S_1) → D'_1
  112. Segment(D, D'_1) → m_2
  113. Segment(C, C'_2) → n_2
  114. Angle(D, S_1, C) → ζ
  115. Dilate(F'_3, If[15 < a ≤ 16, 16 - a, 0], C) → H
  116. Vector(F'_3, H) → v_2
  117. Translate(F, v_2) → F'_4
  118. Translate(F'_3, v_2) → I
  119. Segment(F'_4, I) → p_2
  120. Line(C, j_2) → q_2
  121. Point(q_2) → J
  122. Angle(J, C, C'_2) → η
  123. Rotate(F'_4, If[16 < a ≤ 17, ((a - 16) * η), η], C) → K
  124. Rotate(I, If[16 < a ≤ 17, ((a - 16) * η), η], C) → I'
  125. Segment(K, I') → r_2

AI 绘图提示语参考

绘制一个由两个正方形共享一条边构成的复合图形，其中一个正方形以另一个正方形的顶点为圆心旋转，形成动态的折叠效果。图形中包含圆形、扇形、多边形和线段，并随参数变化展示平移、旋转和缩放。在特定阶段，一个扇形沿向量平移并旋转，同时两个点沿直线移动，形成概率统计的视觉模拟。整体构图强调几何变换与动态过程的结合，适合教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。