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A Variant of Asymmetric Propeller with Varying Equilateral Triangles

A Variant of Asymmetric Propeller with Varying Equilateral Triangles
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2017-04-03 01:27
TrianglePolygonProbability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates an asymmetric propeller pattern constructed from equilateral triangles of varying sizes. It involves core mathematical concepts such as equilateral triangles, stochastic processes, exponential functions, conditional probability, random experiments, LCM, and GCD. The construction utilizes GeoGebra commands like Polygon, Rotate, Ray, Circle, Intersect, Line, and Segment. It is suitable for high school mathematics education, showcasing the integration of geometric transformations and probability statistics.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 3) → poly5, p_1, q_1, r_1, N
  2. Polygon(A, B, C) → poly1, c, a, b
  3. Rotate(D, (-Angle[A, B, C]), A) → D'
  4. Ray(A, D') → f
  5. Circle(A, (Distance[A, D] * Distance[A, B] / Distance[B, C])) → d
  6. Intersect(d, f, 1) → E
  7. Polygon(A, D, E) → poly2, e, a_1, d_1
  8. Rotate(F, (-Angle[B, C, A]), A) → F'
  9. Ray(A, F') → g
  10. Circle(A, (Distance[A, F] * Distance[B, C] / Distance[A, C])) → h
  11. Intersect(h, g, 1) → G
  12. Polygon(G, A, F) → poly3, f_1, g_1, a_2
  13. Line(G, c) → i
  14. Line(B, f_1) → j
  15. Line(C, e) → k
  16. Line(D, b) → l
  17. Line(E, g_1) → m
  18. Line(F, d_1) → n
  19. Intersect(m, n) → H
  20. Intersect(i, j) → I
  21. Segment(G, I) → p
  22. Segment(I, B) → q
  23. Segment(F, H) → s
  24. Segment(H, E) → t
  25. Intersect(k, l) → J
  26. Segment(C, J) → r
  27. Segment(J, D) → h_1
  28. Segment(I, A) → i_1
  29. Segment(A, H) → j_1
  30. Segment(A, J) → k_1
  31. Segment(G, B) → l_1
  32. Segment(C, D) → m_1
  33. Segment(F, E) → n_1
  34. Polygon(K, M, L) → poly4, l_2, k_2, m_2