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Animation 275: Geometric Construction of Ellipse, Angles, and Probability Statis

Animation 275: Geometric Construction of Ellipse, Angles, and Probability Statis
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2017-05-30 05:04
AngleProbability & StatisticsTransformationSlider Animation
This GeoGebra example demonstrates a dynamic geometric construction involving an ellipse, circles, angles, vectors, and elements of probability and statistics. The core mathematical concepts include properties of ellipses, angle rotation, vector translation and scaling, and the geometric representation of statistical characteristics. The construction uses commands such as Circle, Point, Line, Intersect, CircleArc, Segment, Rotate, Angle, Ray, Dilate, Vector, Translate, Min, and CircleSector to build the figure. Numerous objects (A, B, c, C, f, D, d, e, g, h, C', α, j, k, p, F, q, H, I, a, C'_1, i, I', l, m, E, D', n, H', r, F', s, β, C'_2, γ, G, δ, t, b, f_1) are used to create a complex interactive animation. Suitable for high school and above, this example helps students visualize the interplay between ellipse geometry, angle transformations, and probabilistic concepts, and serves as a resource for teachers creating interactive math lessons.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. Intersect(c, f, 2) → D
  5. CircleArc(A, C, D) → d
  6. CircleArc(A, D, C) → e
  7. Segment(A, C) → g
  8. Circle(D, g) → h
  9. Rotate(C, (3 * π / 4), A) → C'
  10. Angle(C, A, C') → α
  11. Ray(A, C') → j
  12. CircleArc(A, C, C') → k
  13. CircleArc(A, C', D) → p
  14. Point(p) → F
  15. Circle(F, g) → q
  16. Intersect(q, f) → H, I
  17. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], A) → C'_1
  18. Segment(C, C'_1) → i
  19. Dilate(I, If[1 < a ≤ 2, 2 - a, 0], D) → I'
  20. Segment(A, I') → l
  21. Ray(H, F) → m
  22. Intersect(k, m, 1) → E
  23. Dilate(D, If[2 < a ≤ 3, 3 - a, 0], H) → D'
  24. Segment(D, D') → n
  25. Dilate(H, If[3 < a ≤ 4, 4 - a, 0], F) → H'
  26. Segment(H, H') → r
  27. Dilate(F, If[4 < a ≤ 5, 5 - a, 0], E) → F'
  28. Segment(F, F') → s
  29. Angle(C, A, E) → β
  30. Rotate(C, β / 3, A) → C'_2
  31. Angle(C, A, C'_2) → γ
  32. Rotate(C'_2, β / 3, A) → G
  33. Angle(C'_2, A, G) → δ
  34. Ray(A, G) → t
  35. Ray(A, C'_2) → b
  36. Ray(A, E) → f_1
  37. Angle(C, H, E) → ε
  38. Rotate(A, If[5 < a ≤ 6, ((a - 5) * ε), ε], D) → A'
  39. Rotate(I', If[5 < a ≤ 6, ((a - 5) * ε), ε], D) → I''
  40. Segment(A', I'') → l'
  41. Dilate(D, If[6 < a ≤ 7, 7 - a, 0], H) → D'_1
  42. Vector(D, D'_1) → u
  43. Translate(A', u) → A''
  44. Translate(I'', u) → I'''
  45. Segment(A'', I''') → l''
  46. Segment(H, D) → g_1
  47. Min(g_1, Distance[A, C]) → o
  48. Circle(A, (0.4 * o)) → c_1
  49. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], E) → A'_1
  50. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], G) → A'_2
  51. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], C'_2) → A'_3
  52. Segment(A, A'_1) → h_1
  53. Segment(A, A'_2) → i_1
  54. Segment(A, A'_3) → j_1
  55. Segment(A, E) → k_1
  56. Segment(A, G) → l_1
  57. Intersect(c_1, k_1, 1) → J
  58. Intersect(c_1, l_1, 1) → K
  59. CircleSector(A, K, J) → d_1
  60. Rotate(d_1, If[9 < a ≤ 10, ((-(a - 9)) * ε), (-ε)], A) → e_1
  61. Rotate(e_1, If[11 < a ≤ 12, ((-(a - 11)) * ε), (-ε)], A) → p_1
  62. Dilate(A, If[13 < a ≤ 14, 14 - a, 0], H) → A'_4
  63. Vector(A, A'_4) → v
  64. Translate(p_1, v) → q_1