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Dynamic GeoGebra Illustration

Dynamic GeoGebra Illustration
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2017-04-23 09:01
VectorTrigonometryCoordinate GeometryParametric EquationGeometric Construction
This example dynamically illustrates a geometric problem posted by Antonio Gutierrez on Twitter, involving logarithms, random variables, isosceles triangles, parametric curves, and real numbers. Key math concepts include logarithmic operations, random variable distributions, properties of isosceles triangles, parametric curve plotting, and real number representation. Construction highlights GeoGebra commands like Rotate, Ray, Point, Polygon, Line, Intersect, Segment, Midpoint, Angle, Min, Circle, CircleSector, Dilate, Vector, Translate, and OrthogonalLine. Suitable for high school and advanced learners to explore dynamic geometric transformations and core concept applications.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Ray(B, A') → g
  3. Point(g) → C
  4. Polygon(B, C, 4) → poly2, n, p, q, r, F, G
  5. Line(A, G) → h_3
  6. Polygon(C, A, 4) → poly1, j, k, l, m, D, E
  7. Line(B, D) → j_2
  8. Intersect(h_3, j_2) → D_1
  9. Rotate(A, If[0 < u ≤ 1, (u * π / 2), π / 2], C) → A'_1
  10. Rotate(C, If[0 < u ≤ 1, (u * π / 2), π / 2], C) → C'
  11. Segment(C', A'_1) → i'
  12. Midpoint(i') → V
  13. Angle(A, B, A') → α
  14. Segment(A, B) → f
  15. Segment(B, C) → h
  16. Segment(C, A) → i
  17. Angle(poly2) → β, γ, δ, ε
  18. Angle(poly1) → ζ, η, θ, ι
  19. Segment(C, E) → s
  20. Segment(E, D) → t
  21. Segment(D, A) → b
  22. Segment(B, G) → c
  23. Segment(G, F) → d
  24. Segment(F, C) → e
  25. Min(i, h) → o
  26. Circle(E, (0.15 * o)) → c_1
  27. Polygon(B, A, C) → poly3, c_2, b_1, a_1
  28. Intersect(c_1, s, 1) → H
  29. Intersect(c_1, t, 1) → I
  30. Line(B, E) → f_1
  31. Line(A, F) → g_1
  32. Line(G, D) → h_1
  33. Circle(A, (0.15 * o)) → d_1
  34. Intersect(d_1, b, 1) → K
  35. Intersect(d_1, i, 1) → L
  36. CircleSector(A, K, L) → e_1
  37. Rotate(B, If[0 < u ≤ 1, (u * π / 2), π / 2], B) → B'
  38. Rotate(C, If[0 < u ≤ 1, (u * π / 2), π / 2], B) → C'_1
  39. Segment(B', C'_1) → h'
  40. Rotate(B', If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], G) → B''
  41. Rotate(C'_1, If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], G) → M
  42. Segment(B'', M) → h''
  43. Rotate(C', If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], E) → C''
  44. Rotate(A'_1, If[1 < u ≤ 2, ((u - 1) * π / 2), π / 2], E) → N
  45. Segment(C'', N) → i''
  46. Rotate(C'', If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], D) → C'''
  47. Rotate(N, If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], D) → N'
  48. Segment(C''', N') → i'''
  49. Rotate(B'', If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], F) → B'''
  50. Rotate(M, If[2 < u ≤ 3, ((u - 2) * π / 2), π / 2], F) → M'
  51. Segment(B''', M') → h'''
  52. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], D) → A'_2
  53. Vector(A, A'_2) → v
  54. Translate(e_1, v) → k_1
  55. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], C) → A'_3
  56. Vector(A, A'_3) → w
  57. Translate(e_1, w) → p_1
  58. Line(C, A) → i_1
  59. Point(i_1) → O
  60. Angle(O, C, F) → κ
  61. Rotate(p_1, If[4.5 < u ≤ 5.5, ((u - 4.5) * (π / 2 + κ)), π / 2 + κ], C) → q_1
  62. Rotate(k_1, If[4.5 < u ≤ 5.5, ((u - 4.5) * π / 2), π / 2], D) → r_1
  63. Dilate(D, If[5.5 < u ≤ 6.5, 6.5 - u, 0], E) → D'
  64. Dilate(C, If[5.5 < u ≤ 6.5, 6.5 - u, 0], F) → C'_2
  65. Vector(C, C'_2) → u_1
  66. Vector(D, D') → v_1
  67. Translate(r_1, v_1) → s_1
  68. Translate(q_1, u_1) → t_1
  69. Rotate(s_1, If[6.5 < u ≤ 7.5, ((u - 6.5) * π / 2), π / 2], E) → d_2
  70. Rotate(t_1, If[6.5 < u ≤ 7.5, ((u - 6.5) * π / 2), π / 2], F) → e_2
  71. Dilate(F, If[7.5 < u ≤ 8.5, 8.5 - u, 0], G) → F'
  72. Dilate(E, If[7.5 < u ≤ 8.5, 8.5 - u, 0], V) → E'
  73. Vector(E, E') → w_1
  74. Vector(F, F') → j_1
  75. Translate(d_2, w_1) → f_2
  76. Translate(e_2, j_1) → g_2
  77. Rotate(g_2, If[8.5 < u ≤ 9.5, ((u - 8.5) * π / 2), π / 2], G) → h_2
  78. Circle(G, 2) → p_2
  79. Circle(D, 2) → q_2
  80. Circle(F, 2) → r_2
  81. Intersect(r_2, g_1, 2) → P
  82. Intersect(p_2, h_1, 1) → Q
  83. Intersect(d_1, g_1, 1) → R
  84. Intersect(q_2, h_1, 2) → S
  85. Circle(B, 2) → s_2
  86. Intersect(s_2, f_1, 1) → T
  87. Intersect(c_1, f_1, 2) → U
  88. Rotate(f_2, If[8.5 < u ≤ 9.5, ((u - 8.5) * π / 2), π / 2], V) → k_2
  89. Dilate(V, If[9.5 < u ≤ 10.5, 10.5 - u, 0], C) → V'
  90. Vector(V, V') → u_2
  91. Translate(k_2, u_2) → t_2
  92. Dilate(B, If[11 < u ≤ 12, 12 - u, 0], D) → B'_1
  93. Segment(B, B'_1) → m_2
  94. Dilate(A, If[12 < u ≤ 13, 13 - u, 0], D_1) → A'_4
  95. Segment(A, A'_4) → n_2
  96. Dilate(D_1, If[13 < u ≤ 14, 14 - u, 0], G) → J'
  97. Line(G, n_2) → g_3
  98. Point(g_3) → A_1
  99. Angle(F, G, A_1) → λ
  100. Circle(B, (0.15 * o)) → r_3
  101. Intersect(r_3, f, 1) → B_1
  102. Intersect(r_3, h, 1) → C_1
  103. CircleSector(B, B_1, C_1) → s_3
  104. Line(C, D_1) → i_3
  105. Line(B, A) → j_3
  106. Intersect(j_3, i_3) → E_1
  107. Segment(D_1, J') → a_2
  108. Dilate(C, If[14 < u ≤ 15, 15 - u, 0], D_1) → C'_3
  109. Segment(C, C'_3) → m_1
  110. Dilate(D_1, If[15 < u ≤ 16, 16 - u, 0], E_1) → J
  111. Segment(D_1, J) → n_1
  112. OrthogonalLine(C, j_3) → i_2
  113. Intersect(j_3, i_2) → W
  114. Dilate(A, If[16 < u ≤ 17, 17 - u, 0], W) → A'_5
  115. Vector(A, A'_5) → l_1
  116. Translate(e_1, l_1) → c_3
  117. Line(A, m_1) → l_2
  118. Point(j_3) → Z
  119. Angle(Z, A, D) → μ
  120. Rotate(c_3, If[16 < u ≤ 17, ((-(u - 16)) * μ), (-μ)], W) → d_3