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Animation Demonstrating Geometric Transformations and Probability

Animation Demonstrating Geometric Transformations and Probability
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2016-06-26 08:24
CircleSolid GeometryProbability & StatisticsTransformationGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D
This example demonstrates geometric transformations like rotation, dilation, and probability distributions involving circles through animations. Core concepts include circle, probability, centroid, prism, hypergeometric distribution, and planes. GeoGebra commands like Center, Rotate, Angle, CircleArc, Dilate, Segment, and Point are used in the construction. Suitable for high school and above students to explore solid geometry, probability & statistics, and the integration of geometric transformations.

GeoGebra Commands & Parameters

  1. Center(c) → B
  2. Rotate(A, 1, B) → A'
  3. Angle(A, B, A') → α
  4. Rotate(A', 1, B) → A''
  5. Angle(A', B, A'') → β
  6. Rotate(A'', 1, B) → A'''
  7. Angle(A'', B, A''') → γ
  8. Rotate(A''', 1, B) → C
  9. Angle(A''', B, C) → δ
  10. Rotate(C, 1, B) → C'
  11. Angle(C, B, C') → ε
  12. Rotate(C', 1, B) → C''
  13. Angle(C', B, C'') → ζ
  14. CircleArc(B, A, A') → d
  15. CircleArc(B, A', A'') → e
  16. CircleArc(B, A'', A''') → f
  17. CircleArc(B, A''', C) → g
  18. CircleArc(B, C, C') → h
  19. CircleArc(B, C', C'') → k
  20. Rotate(A, If[0 ≤ a ≤ 1, (a * α), α], B) → A'_1
  21. CircleArc(B, A, A'_1) → p
  22. Dilate(B, If[0 ≤ a ≤ 1, 1 - a, 0], A) → B'
  23. Segment(B', A) → b
  24. CircleArc(B, C'', A) → q
  25. CircleArc(B, A'_1, A') → s
  26. Segment(B, B') → j
  27. Segment(B, A') → l
  28. Point(h) → D
  29. Segment(B, D) → Radius
  30. Rotate(B', If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → B''
  31. Rotate(d, If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → d'
  32. CircleArc(B, A, B'') → t
  33. Dilate(B, If[1.2 ≤ a ≤ 2.2, 2.2 - a, 0], A) → B'_1
  34. Segment(B'_1, A) → m
  35. Segment(B, B'_1) → n
  36. Dilate(B, If[2.4 ≤ a ≤ 3.4, 3.4 - a, 0], A) → B'_2
  37. Segment(B, B'_2) → a_1
  38. Segment(B'_2, A) → b_1
  39. Rotate(d', If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → d''
  40. Rotate(t, If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → t'
  41. Rotate(A, If[2.4 < a < 3.4, ((a - 2.4) * β), β], B) → A'_2
  42. CircleArc(B, A, A'_2) → c_1
  43. Dilate(B, If[3.6 ≤ a ≤ 4.6, 4.6 - a, 0], A) → B'_3
  44. Segment(B'_3, A) → d_1
  45. Segment(B, B'_3) → e_1
  46. Rotate(A, If[3.6 < a < 4.6, ((a - 3.6) * β), β], B) → A'_3
  47. CircleArc(B, A, A'_3) → f_1
  48. Rotate(d'', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → d'''
  49. Rotate(t', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → t''
  50. Rotate(c_1, If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → g_1
  51. Dilate(B, If[4.8 ≤ a ≤ 5.8, 5.8 - a, 0], A) → B'_4
  52. Segment(B, B'_4) → h_1
  53. Segment(B'_4, A) → i_1
  54. Rotate(d''', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → k_1
  55. Rotate(t'', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → t'''
  56. Rotate(g_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → p_1
  57. Rotate(f_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → q_1
  58. Rotate(A, If[4.8 < a < 5.8, ((a - 4.8) * β), β], B) → A'_4
  59. CircleArc(B, A, A'_4) → r_1
  60. Dilate(B, If[6 ≤ a ≤ 7, 7 - a, 0], A) → B'_5
  61. Segment(B'_5, A) → j_1
  62. Segment(B, B'_5) → l_1
  63. Rotate(A, If[6 < a < 7, ((a - 6) * β), β], B) → A'_5
  64. CircleArc(B, A, A'_5) → s_1
  65. Rotate(k_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → t_1
  66. Rotate(t''', If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → c_2
  67. Rotate(p_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → d_2
  68. Rotate(q_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → e_2
  69. Rotate(r_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → f_2
  70. CircleArc(B, C'', A) → g_2