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Asymmetric Propeller

Asymmetric Propeller
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2017-08-10 20:30
TrianglePolygonGeometric Construction
This example demonstrates the geometric construction and dynamic variation of an asymmetric propeller. It involves core mathematical concepts such as Similar Triangles, Triangles, Scatter Plot, Random Experiments, Orthocenter, Normal Distribution, and Integers. The construction utilizes GeoGebra commands and objects like Polygon, Rotate, Ray, Line, Intersect, Segment, Angle, Midpoint, and PointIn. It is suitable for high school mathematics education, showcasing the integration of geometric transformations and data analysis.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Rotate(C', β, B) → C''
  3. Ray(B, C'') → m
  4. Line(C, B') → k_2
  5. Rotate(A, (-β), B') → A'_1
  6. Ray(B', A'_1) → i
  7. Rotate(B', α, A) → B''
  8. Ray(A, B'') → j
  9. Intersect(i, j) → C_1
  10. Rotate(B, (-Angle[A, C_1, B']), C') → B'_1
  11. Ray(C', B'_1) → n
  12. Intersect(m, n) → A_1
  13. Line(A_1, C') → n_2
  14. Segment(A, B') → f
  15. Segment(C', B) → g
  16. Segment(C, A') → h
  17. Segment(A, C_1) → k
  18. Segment(B', C_1) → l
  19. Segment(C', A_1) → p
  20. Segment(A_1, B) → q
  21. Rotate(A', Angle[A, C_1, B'], C) → A''
  22. Ray(C, A'') → r
  23. Rotate(C, (-α), A') → C'_1
  24. Ray(A', C'_1) → s
  25. Intersect(r, s) → B_1
  26. Segment(C, B_1) → t
  27. Segment(A', B_1) → d
  28. Segment(A_1, C_1) → e
  29. Segment(B_1, C_1) → f_1
  30. Segment(A_1, B_1) → g_1
  31. Angle(B, A_1, C') → γ
  32. Angle(B', A, C_1) → δ
  33. Angle(B_1, A', C) → ε
  34. Angle(C_1, B', A) → ζ
  35. Angle(C, B_1, A') → η
  36. Angle(C', B, A_1) → θ
  37. Angle(B_1, A_1, C_1) → ι
  38. Rotate(A, Angle[A, C_1, B'], C') → A'_2
  39. Ray(C', A'_2) → h_1
  40. Rotate(C', (-α), A) → C''_1
  41. Ray(A, C''_1) → i_1
  42. Intersect(h_1, i_1) → B_2
  43. Segment(C', B_2) → j_1
  44. Segment(B_2, A) → k_1
  45. Segment(A, C') → l_1
  46. Rotate(B', (-Angle[A, C_1, B']), C) → B''_1
  47. Ray(C, B''_1) → m_1
  48. Rotate(C, β, B') → C'_2
  49. Ray(B', C'_2) → n_1
  50. Intersect(m_1, n_1) → A_2
  51. Segment(B', A_2) → p_1
  52. Segment(C, A_2) → q_1
  53. Segment(C, B') → r_1
  54. Rotate(B, α, A') → B'_2
  55. Ray(A', B'_2) → s_1
  56. Rotate(A', (-β), B) → A''_1
  57. Ray(B, A''_1) → t_1
  58. Intersect(s_1, t_1) → C_2
  59. Segment(B, C_2) → a_1
  60. Segment(C_2, A') → b_1
  61. Segment(A', B) → c_1
  62. Angle(B_1, A_1, C_1) → κ
  63. Angle(C_1, B_1, A_1) → μ
  64. Angle(C', B_2, A) → ν
  65. Angle(C, B', A_2) → ξ
  66. Angle(C_2, B, A') → ο
  67. Angle(B_2, A, C') → ρ
  68. Angle(B', A_2, C) → σ
  69. Angle(B, A', C_2) → τ
  70. Segment(B_2, C_2) → d_1
  71. Segment(C_2, A_2) → e_1
  72. Segment(A_2, B_2) → f_2
  73. Midpoint(A_1, B_1) → E_1
  74. Midpoint(B_1, C_1) → F_1
  75. Segment(A_1, F_1) → g_2
  76. Segment(C_1, E_1) → h_2
  77. Intersect(g_2, h_2) → G
  78. Midpoint(B_2, A_2) → H
  79. Midpoint(A_2, C_2) → I
  80. Segment(B_2, I) → i_2
  81. Segment(C_2, H) → j_2
  82. Intersect(i_2, j_2) → J
  83. PointIn(poly1) → K
  84. Line(A, C') → l_2
  85. Line(C, B_1) → m_2
  86. Intersect(l_2, m_2) → E
  87. Intersect(k_2, n_2) → F
  88. Angle(C', F, C) → υ
  89. Angle(C', E, C) → ϕ
  90. Angle(A_1, C', A) → χ
  91. Angle(B', C, B_1) → ψ
  92. Midpoint(B, B') → P
  93. Segment(B', B) → p_2
  94. Segment(C', C) → q_2
  95. Segment(A', A) → r_2