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Animation Demonstrating Geometric Transformations and Probability Distributions

Animation Demonstrating Geometric Transformations and Probability Distributions
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2017-04-30 09:35
Probability & StatisticsTransformationGeometric ConstructionGraphing
This example dynamically illustrates geometric transformations and probability distributions through animation. Key math concepts include geometric transformations (rotation, translation, dilation), probability & statistics (normal distribution, geometric distribution, percentages), and data visualization (histogram). Construction highlights involve commands/objects like Segment, OrthogonalLine, Point, Ray, Angle, Circle, Intersect, Rotate, Midpoint, Polygon, Min, CircleSector, Dilate, Vector, Translate from GeoGebra. Suitable for high school and above, enhancing spatial visualization and data analysis skills in geometry and probability.

GeoGebra Commands & Parameters

  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