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Dynamic Illustration of an Equilateral Triangle Problem

Dynamic Illustration of an Equilateral Triangle Problem
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2018-01-02 11:02
TriangleVectorGeometric Construction
This is a dynamic and modifiable illustration of an equilateral triangle problem posted by Antonio Gutierrez on Twitter. The example demonstrates the basic properties and dynamic transformations of an equilateral triangle. Using GeoGebra commands such as Distance, PointIn, Line, Circle, Intersect, Rotate, CircleArc, OrthogonalLine, Point, Polygon, Semicircle, Segment, Angle, Dilate, Vector, Translate, one can observe the properties and transformations of the equilateral triangle. Suitable for students at the junior high school level and above to learn about geometric transformations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Distance(A, B) → a
  2. PointIn(b) → C
  3. Line(C, A) → f
  4. Circle(A, B) → c
  5. Intersect(c, f) → D, E
  6. Rotate(D, (-2 * π / 3), A) → D'
  7. Rotate(D', (-2 * π / 3), A) → D''
  8. CircleArc(A, D'', D') → q
  9. OrthogonalLine(D, f) → g
  10. Point(q) → F
  11. Rotate(F, (2 * π / 3), A) → F'
  12. Rotate(F', (2 * π / 3), A) → F''
  13. Polygon(F, F', F'') → t1, f'', f_1, f'
  14. Semicircle(C, F') → e
  15. Semicircle(F'', C) → h
  16. Intersect(d, e, 1) → I
  17. Intersect(d, h, 1) → J
  18. Segment(F', I) → i
  19. Segment(F'', J) → j
  20. Semicircle(F, C) → k
  21. Intersect(d, k, 1) → K
  22. Segment(F, K) → l
  23. Angle(F'', J, C) → α
  24. Angle(C, I, F') → β
  25. Angle(F, K, C) → γ
  26. Circle(F, i) → p
  27. Intersect(p, l, 1) → G
  28. Dilate(F, If[0 < n ≤ 1, 1 - n, 0], F') → F'_1
  29. Segment(F, F'_1) → r
  30. Rotate(F, If[1 < n ≤ 2, ((n - 1) * π / 3), π / 3], F) → F'_2
  31. Rotate(F'_1, If[1 < n ≤ 2, ((n - 1) * π / 3), π / 3], F) → H
  32. Segment(F'_2, H) → r'
  33. Rotate(F, If[2 < n ≤ 3, ((-(n - 2)) * π / 3), ((-π)) / 3], F') → F'_3
  34. Rotate(F'_1, If[2 < n ≤ 3, ((-(n - 2)) * π / 3), ((-π)) / 3], F') → L
  35. Segment(F'_3, L) → r'_1
  36. Dilate(C, If[3 < n ≤ 4, 4 - n, 0], I) → C'
  37. Dilate(F', If[3 < n ≤ 4, 4 - n, 0], I) → F''_1
  38. Segment(F', F''_1) → s
  39. Segment(C, C') → t
  40. Dilate(F'', If[4 < n ≤ 5, 5 - n, 0], J) → F'''
  41. Segment(F'', F''') → g_1
  42. Dilate(C, If[4 < n ≤ 5, 5 - n, 0], J) → C'_1
  43. Segment(C, C'_1) → h_1
  44. Dilate(F, If[5 < n ≤ 6, 6 - n, 0], G) → F'_4
  45. Segment(F, F'_4) → i_1
  46. Dilate(G, If[6 < n ≤ 7, 7 - n, 0], K) → G'
  47. Segment(G, G') → j_1
  48. Dilate(C, If[6 < n ≤ 7, 7 - n, 0], K) → C'_2
  49. Segment(C, C'_2) → k_1
  50. Dilate(F', If[8 < n ≤ 9, 9 - n, 0], F) → F''_2
  51. Vector(F', F''_2) → u
  52. Translate(F', u) → F''_3
  53. Translate(F''_1, u) → M
  54. Segment(F''_3, M) → s'
  55. Line(F', j_1) → l_1
  56. Point(l_1) → N
  57. Angle(I, F', N) → δ
  58. Rotate(F''_3, If[9 < n ≤ 10, ((n - 9) * δ), δ], F) → O
  59. Rotate(M, If[9 < n ≤ 10, ((n - 9) * δ), δ], F) → M'
  60. Segment(O, M') → s''
  61. Dilate(J, If[10 < n ≤ 11, 11 - n, 0], K) → J'
  62. Vector(J, J') → v
  63. Translate(F'', v) → F'''_1
  64. Translate(F''', v) → P
  65. Segment(F'''_1, P) → m_1
  66. Line(J, j_1) → n_1
  67. Point(n_1) → Q
  68. Angle(F'', J, Q) → ε
  69. Rotate(F'''_1, If[11 < n ≤ 12, ((n - 11) * ε), ε], K) → R
  70. Rotate(P, If[11 < n ≤ 12, ((n - 11) * ε), ε], K) → P'
  71. Segment(R, P') → p_1