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A Variant of Asymmetric Propeller with Equilateral Triangles

A Variant of Asymmetric Propeller with Equilateral Triangles
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2017-04-03 01:33
TrianglePolygonMatrixGeometric Construction
This example demonstrates an asymmetric propeller composed of equal-sized equilateral triangles. Core math concepts include equilateral triangles, rotation, angles, and matrix transformations. Construction highlights involve commands like Circle, Polygon, Point, Rotate, Ray, Intersect, Line, and Segment in GeoGebra. Suitable for high school and above students to explore geometric transformations and polygon combinations.

GeoGebra Commands & Parameters

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