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Dynamic Geometric Illustration by Tim Brzezinski (2)

Dynamic Geometric Illustration by Tim Brzezinski (2)
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2019-01-21 08:45
FunctionOptimizationSlider Animation
This example dynamically illustrates a geometric problem posed by Antonio Gutierrez, involving core mathematical concepts such as logarithmic functions, parabolas, Pythagoras' theorem, and linear programming. Constructed using GeoGebra commands like Segment, Rotate, Angle, Ray, Point, Polygon, Line, Circle, Intersect, Min, CircleSector, Dilate, Vector, and Translate, it demonstrates the process of geometric construction and transformation. Suitable for high school and above, this visualization helps understand complex geometric problems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Polygon(A, C, B) → t1, b, a_1, c
  7. Segment(A, C) → h
  8. Segment(C, B) → i
  9. Line(A, i) → j
  10. Line(B, h) → k
  11. Circle(A, 2) → d
  12. Intersect(d, j) → D, E
  13. Ray(A, D) → l
  14. Point(l) → F
  15. Circle(B, Distance[A, F]) → e
  16. Intersect(e, k, 2) → G
  17. Segment(B, G) → m
  18. Ray(A, G) → n
  19. Ray(B, F) → p
  20. Intersect(n, p) → H
  21. Ray(C, H) → q
  22. Angle(A, C, H) → β
  23. Angle(H, C, B) → γ
  24. Circle(B, 2) → r
  25. Line(A, B) → s
  26. Intersect(d, s, 1) → I
  27. Intersect(r, s) → J, K
  28. Ray(A, I) → t
  29. Ray(B, K) → f_1
  30. Ray(B, G) → g_1
  31. Min({f, h, i}) → o
  32. Circle(A, (0.2 * o)) → c_1
  33. Circle(B, (0.2 * o)) → d_1
  34. Intersect(c_1, f, 1) → L
  35. Intersect(d_1, i, 1) → M
  36. Rotate(M, If[0 < u ≤ 1, (u * (π - α - (2 * β))), π - α - (2 * β)], B) → M'
  37. Intersect(d_1, f_1, 1) → N
  38. CircleSector(B, M, M') → e_1
  39. Dilate(B, If[1.5 < u ≤ 2.5, 2.5 - u, 0], A) → B'_1
  40. Vector(B, B'_1) → v
  41. Translate(e_1, v) → h_1
  42. Rotate(N, If[3 < u ≤ 4, ((u - 3) * α), α], B) → N'
  43. CircleSector(B, N, N') → k_1
  44. Dilate(B, If[4.5 < u ≤ 5.5, 5.5 - u, 0], A) → B'_2
  45. Vector(B, B'_2) → w
  46. Translate(k_1, w) → p_1
  47. Dilate(A, If[7 < u ≤ 8, 8 - u, 0], F) → A'
  48. Segment(A, A') → i_1
  49. Dilate(A, If[8.5 < u ≤ 9.5, 9.5 - u, 0], B) → A'_1
  50. Vector(A, A'_1) → u_1
  51. Translate(A, u_1) → A'_2
  52. Translate(A', u_1) → A''
  53. Segment(A'_2, A'') → j_1
  54. Angle(G, B, A'') → δ
  55. Rotate(A'_2, If[9.5 < u ≤ 10.5, ((-(u - 9.5)) * δ), (-δ)], B) → O
  56. Rotate(A'', If[9.5 < u ≤ 10.5, ((-(u - 9.5)) * δ), (-δ)], B) → A'''
  57. Segment(O, A''') → l_1
  58. Dilate(F, If[11.5 < u ≤ 12.5, 12.5 - u, 0], B) → F'
  59. Segment(F, F') → m_1
  60. Dilate(G, If[12.5 < u ≤ 13.5, 13.5 - u, 0], H) → G'
  61. Segment(G, G') → n_1
  62. Dilate(H, If[13.5 < u ≤ 14.5, 14.5 - u, 0], A) → H'
  63. Segment(H, H') → q_1
  64. Ray(C, H) → r_1
  65. Circle(C, (0.3 * o)) → s_1
  66. Intersect(s_1, h) → P,
  67. Dilate(C, If[14.5 < u ≤ 15.5, 15.5 - u, 0], H) → C'
  68. Segment(C, C') → t_1
  69. Rotate(P, If[16 < u ≤ 17, ((u - 16) * γ), γ], C) → P'
  70. CircleSector(C, P, P') → c_2
  71. Rotate(c_2, If[18 < u ≤ 19, ((u - 18) * γ), γ], C) → d_2