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Rotation Animation of an Equilateral Triangle

Rotation Animation of an Equilateral Triangle
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2016-09-10 11:09
TriangleTrigonometry
In collections CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates the rotation of an equilateral triangle around its vertices. Key mathematical concepts include the properties of equilateral triangles, rotation transformations, and angle measurement. Using GeoGebra commands such as Rotate, Polygon, and Angle, the animation provides a visual representation of the rotation. Suitable for middle school and above students to learn geometric transformations and trigonometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → p
  2. PointIn(d) → C
  3. Polygon(A, B, C) → poly1, c, a, b
  4. Angle(poly1) → α, β, γ
  5. Rotate(B, α / 3, A) → B'
  6. Angle(B, A, B') → δ
  7. Ray(A, B') → f
  8. Rotate(B', α / 3, A) → B''
  9. Angle(B', A, B'') → ε
  10. Ray(A, B'') → g
  11. Rotate(C, β / 3, B) → C'
  12. Angle(C, B, C') → ζ
  13. Ray(B, C') → h
  14. Rotate(C', β / 3, B) → C''
  15. Angle(C', B, C'') → η
  16. Ray(B, C'') → i
  17. Rotate(A, γ / 3, C) → A'
  18. Angle(A, C, A') → θ
  19. Ray(C, A') → j
  20. Rotate(A', γ / 3, C) → A''
  21. Angle(A', C, A'') → ι
  22. Ray(C, A'') → k
  23. Intersect(f, i) → D
  24. Intersect(h, k) → E
  25. Intersect(g, j) → F
  26. Segment(D, E) → l
  27. Segment(E, F) → m
  28. Segment(F, D) → n
  29. Line(A, C) → q
  30. Line(C, B) → r
  31. Min({a, b, c}) → s
  32. Segment(A, B) → t
  33. Segment(B, C) → f_1
  34. Segment(C, A) → g_1
  35. Intersect(g, f_1) → G
  36. Intersect(f, f_1) → H
  37. Intersect(g_1, h) → I
  38. Intersect(g_1, i) → J
  39. Intersect(k, t) → K
  40. Intersect(j, t) → L
  41. Circle(A, (0.2 * s)) → c_1
  42. Circle(B, (0.2 * s)) → d_1
  43. Circle(C, (0.2 * s)) → e_1
  44. Intersect(d_1, f_1, 1) → M
  45. Intersect(d_1, h) → N,
  46. Intersect(c_1, f, 1) → O
  47. Intersect(c_1, t, 1) → P
  48. Intersect(e_1, g_1, 1) → Q
  49. Intersect(e_1, j, 1) → R
  50. CircleSector(B, M, N) → h_1
  51. CircleSector(A, P, O) → k_1
  52. CircleSector(C, Q, R) → p_1
  53. Polygon(D, E, F) → poly2, f_2, d_2, e_2
  54. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'_1
  55. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], E) → B'_1
  56. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], F) → C'_1
  57. Segment(A, A'_1) → i_1
  58. Segment(B, B'_1) → j_1
  59. Segment(C, C'_1) → l_1
  60. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], F) → A'_2
  61. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], D) → B'_2
  62. Dilate(C, If[1 < u ≤ 2, 2 - u, 0], E) → C'_2
  63. Segment(A, A'_2) → m_1
  64. Segment(C, C'_2) → n_1
  65. Segment(B, B'_2) → q_1
  66. Rotate(k_1, If[2 < u ≤ 3, (((u - 2) * 2) * α / 3), (2 * α / 3)], A) → r_1
  67. Rotate(r_1, If[3.5 < u ≤ 4.5, ((-(u - 3.5)) * α / 3), ((-α)) / 3], A) → s_1
  68. Rotate(h_1, If[4.5 < u ≤ 5.5, (((u - 4.5) * 2) * β / 3), (2 * β / 3)], B) → t_1
  69. Rotate(t_1, If[6 < u ≤ 7, ((-(u - 6)) * β / 3), ((-β)) / 3], B) → c_2
  70. Rotate(p_1, If[7 < u ≤ 8, (((u - 7) * 2) * γ / 3), (2 * γ / 3)], C) → g_2
  71. Rotate(g_2, If[8.5 < u ≤ 9.5, ((-(u - 8.5)) * γ / 3), ((-γ)) / 3], C) → h_2
  72. Dilate(D, If[11 < u ≤ 12, 12 - u, 0], E) → D'
  73. Segment(D, D') → a_1
  74. Rotate(D, If[12 < u ≤ 13, ((u - 12) * π / 3), π / 3], D) → D'_1
  75. Rotate(D', If[12 < u ≤ 13, ((u - 12) * π / 3), π / 3], D) → D''
  76. Segment(D'_1, D'') → b_1
  77. Rotate(D'_1, If[13 < u ≤ 14, ((u - 13) * π / 3), π / 3], F) → S
  78. Rotate(D'', If[13 < u ≤ 14, ((u - 13) * π / 3), π / 3], F) → D'''
  79. Segment(S, D''') → i_2