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动画演示几何变换与概率分布

动画演示几何变换与概率分布
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2017-04-30 09:35
概率统计变换几何作图函数图像
①本范例通过动画演示几何图形的变换与概率分布的动态变化；②涉及的核心数学概念包括几何变换（旋转、平移、缩放）、概率统计（正态分布、几何分布、百分比）、数据可视化（直方图）；③作图要点提炼自构造摘要，使用了Segment, OrthogonalLine, Point, Ray, Angle, Circle, Intersect, Rotate, Midpoint, Polygon, Min, CircleSector, Dilate, Vector, Translate等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解几何变换与概率统计的直观表现，增强空间想象与数据分析能力。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. Point(g) → C
  4. Ray(A, C) → h
  5. Ray(A, C) → i
  6. Point(i) → D
  7. Segment(A, D) → j
  8. Segment(D, B) → k
  9. Angle(B, A, D) → α
  10. Circle(B, j) → c
  11. Intersect(c, k, 1) → E
  12. Segment(B, E) → l
  13. Segment(D, E) → m
  14. OrthogonalLine(E, j) → n
  15. Angle(A, D, E) → β
  16. Rotate(A, β / 2, D) → A'
  17. Angle(A, D, A') → γ
  18. Ray(D, A') → p
  19. Intersect(n, p) → F
  20. Midpoint(m) → G
  21. Intersect(n, j) → H
  22. Segment(A, E) → r
  23. Segment(G, F) → q
  24. Segment(F, A) → s
  25. Intersect(p, r) → I
  26. OrthogonalLine(B, f) → t
  27. Point(t) → J
  28. Angle(J, B, E) → δ
  29. Polygon(D, A, E) → poly1, e, d, a
  30. Polygon(A, B, E) → poly2, e_1, a_1, b
  31. Segment(D, H) → f_1
  32. Segment(D, G) → g_1
  33. Min(f_1, g_1) → o
  34. Circle(D, (0.6 * o)) → c_1
  35. Segment(D, E) → h_1
  36. Intersect(c_1, h_1, 1) → K
  37. Intersect(c_1, j, 1) → L
  38. Intersect(c_1, p, 1) → M
  39. CircleSector(D, L, M) → d_1
  40. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'_1
  41. Vector(A, A'_1) → v
  42. Translate(A, v) → A'_2
  43. Translate(D, v) → D'
  44. Segment(A'_2, D') → j'
  45. Rotate(A'_2, If[1 < u ≤ 2, ((u - 1) * δ), δ], B) → N
  46. Rotate(D', If[1 < u ≤ 2, ((u - 1) * δ), δ], B) → D''
  47. Segment(N, D'') → j''
  48. Dilate(E, If[2 < u ≤ 3, 3 - u, 0], G) → E'
  49. Segment(E, E') → i_1
  50. Rotate(E, If[3 < u ≤ 4, ((u - 3) * π), π], G) → E'_1
  51. Rotate(E', If[3 < u ≤ 4, ((u - 3) * π), π], G) → E''
  52. Segment(E'_1, E'') → j_1
  53. Dilate(A, If[4 < u ≤ 5, 5 - u, 0], E) → A'_3
  54. Segment(A, A'_3) → k_1
  55. Polygon(A, E, D) → poly3, d_2, a_2, e_2
  56. Segment(E, H) → l_1
  57. Angle(A, H, E) → ε
  58. Dilate(E, If[5 < u ≤ 6, 6 - u, 0], H) → E'_2
  59. Segment(E, E'_2) → m_1
  60. Dilate(D, If[6 < u ≤ 7, 7 - u, 0], F) → D'_1
  61. Segment(D, D'_1) → n_1
  62. Dilate(F, If[7 < u ≤ 8, 8 - u, 0], I) → F'
  63. Segment(F, F') → p_1
  64. Rotate(d_1, If[8 < u ≤ 9, ((u - 8) * γ), γ], D) → q_1
  65. Dilate(A, If[9 < u ≤ 10, 10 - u, 0], F) → A'_4
  66. Segment(A, A'_4) → r_1
  67. Dilate(F, If[10 < u ≤ 11, 11 - u, 0], G) → F'_1
  68. Segment(FF, F'_1) → s_1