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Dynamic Geometry Problem Demonstration by Tim Brzezinski

Dynamic Geometry Problem Demonstration by Tim Brzezinski
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2017-12-18 06:26
FunctionLimitProbability & StatisticsParametric EquationGeometric Construction
This example dynamically demonstrates a geometry problem posted by Antonio Gutierrez on Twitter. It involves core mathematical concepts such as limits, function graphs, random variables, conditional probability, and parametric curves. Construction highlights include using GeoGebra commands and objects like Midpoint, Segment, Circle, OrthogonalLine, Intersect, Ray, Point, Angle, Rotate, Polygon, Line, Min, Dilate, CircleSector, Vector, and Translate. Suitable for high school and above, helping learners understand the dynamic changes in complex geometric problems.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → H
  2. Segment(A, H) → r
  3. Circle(A, 2) → c
  4. Segment(A, B) → f
  5. OrthogonalLine(A, f) → g
  6. Intersect(c, g, 2) → C
  7. Ray(A, C) → h
  8. Point(h) → D
  9. Segment(D, B) → i
  10. OrthogonalLine(A, i) → m
  11. Intersect(m, i) → G
  12. Angle(G, H, A) → β
  13. Rotate(G, β / 2, H) → G'
  14. Ray(H, G') → t
  15. Segment(G, H) → s
  16. Segment(A, G) → q
  17. Intersect(q, t) → I
  18. Midpoint(H, I) → J
  19. Segment(H, J) → i_1
  20. Segment(H, I) → f_1
  21. Segment(G, B) → p
  22. Segment(D, G) → n
  23. Segment(A, D) → j
  24. Polygon(A, B, D) → t1, d, a, b
  25. Line(B, A) → k
  26. Circle(A, 2) → e
  27. Intersect(e, k) → E, F
  28. Ray(A, F) → l
  29. Angle(D, A, F) → α
  30. Min({n, p, q, r, f_1, s, i_1}) → o
  31. Angle(G, H, G') → γ
  32. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], H) → A'
  33. Segment(A, A') → g_1
  34. Rotate(A, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], H) → A'_1
  35. Rotate(A', If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], H) → A''
  36. Segment(A'_1, A'') → h_1
  37. Dilate(H, If[2 < u ≤ 3, 3 - u, 0], G) → H'
  38. Segment(H, H') → j_1
  39. Dilate(H, If[3 < u ≤ 4, 4 - u, 0], J) → H'_1
  40. Segment(H, H'_1) → k_1
  41. Circle(H, (0.45 * o)) → c_1
  42. Segment(G, H) → l_1
  43. Line(J, H) → m_1
  44. Intersect(c_1, m_1) → K, L
  45. Intersect(c_1, l_1) → M,
  46. Rotate(M, If[5 < u ≤ 6, ((u - 5) * γ), γ], H) → M'
  47. CircleSector(H, M, M') → d_1
  48. Rotate(d_1, If[7 < u ≤ 8, ((u - 7) * γ), γ], H) → e_1
  49. Midpoint(A, G) → N
  50. Dilate(H, If[8 < u ≤ 9, 9 - u, 0], N) → H'_2
  51. Vector(H, H'_2) → v
  52. Translate(e_1, v) → p_1
  53. Rotate(p_1, If[9 < u ≤ 10, ((-(u - 9)) * π / 2), ((-π)) / 2], N) → q_1
  54. Dilate(N, If[10 < u ≤ 11, 11 - u, 0], A) → N'
  55. Vector(N, N') → w
  56. Translate(q_1, w) → r_1
  57. Dilate(A, If[11 < u ≤ 12, 12 - u, 0], G) → A'_2
  58. Segment(A, A'_2) → n_1
  59. Circle(G, (0.45 * o)) → s_1
  60. Intersect(s_1, i, 2) → O
  61. Rotate(O, If[12.5 < u ≤ 13.5, ((-(u - 12.5)) * π / 2), ((-π)) / 2], G) → D'
  62. CircleSector(G, D', O) → t_1
  63. Rotate(t_1, If[14.5 < u ≤ 15.5, ((-(u - 14.5)) * π / 2), ((-π)) / 2], G) → c_2
  64. Rotate(A'_1, If[16 < u ≤ 17, ((u - 16) * (π - β)), π - β], H) → P
  65. Rotate(A'', If[16 < u ≤ 17, ((u - 16) * (π - β)), π - β], H) → A'''
  66. Segment(P, A''') → a_1